Mastering Sets: A Comprehensive Collection of 300 Intriguing Questions and Answers for Class XII Students to Conquer Set Theory with Confidence

Introduction to Sets

• Definition: A set is a well-defined collection of distinct objects.
• Notations: Sets are usually denoted by capital letters (e.g., A, B, C), and elements are enclosed in curly braces (e.g., A = {1, 2, 3}).
• Types of Sets: Finite, Infinite, Equal, Null, Singleton, Subset, and Universal sets.

Formulas:

• Union of Sets: $A \cup B$
• Intersection of Sets: $A \cap B$
• Difference of Sets: $A - B$
• Complement of a Set: $A'$
• Number of Elements in Union of Sets: $|A \cup B| = |A| + |B| - |A \cap B|$
• Number of Elements in Intersection of Sets: $|A \cap B|$

 

Comprehensive Sets Practice Questions for Class XII

Questions 1 to 50

• 1. If A = {1, 2, 3} and B = {3, 4, 5}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5}
• 2. If A = {2, 4, 6} and B = {1, 2, 3, 4}, find A ∩ B.
  A ∩ B = {2, 4}
• 3. If A = {a, b, c} and B = {b, c, d}, find A - B.
  A - B = {a}
• 4. Find the number of elements in the set A = {x | x is an even number less than 10}.
  A = {2, 4, 6, 8}; Number of elements = 4
• 5. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find |A ∪ B|.
  |A ∪ B| = 6
• 6. If A = {x | x is an integer} and B = {x | x is a positive integer}, find A ∩ B.
  A ∩ B = {1, 2, 3, ...}
• 7. Given A = {2, 3, 5} and B = {1, 3, 5}, find A - B and B - A.
  A - B = {2}; B - A = {1}
• 8. If U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, find the complement of A.
  A' = {1, 3, 5}
• 9. Find the symmetric difference of A = {1, 2, 3} and B = {2, 3, 4}.
  A Δ B = {1, 4}
• 10. If A = {1, 2, 3} and B = {2, 3, 4}, find the number of elements in A ∪ B.
  Number of elements = 4
• 11. If A = {1, 2} and B = {2, 3}, find A ∩ B.
  A ∩ B = {2}
• 12. Determine if {1, 2} is a subset of {1, 2, 3}.
  Yes, {1, 2} ⊆ {1, 2, 3}
• 13. If A = {a, b, c} and B = {b, c, d}, find A ∪ B.
  A ∪ B = {a, b, c, d}
• 14. Find the number of elements in the power set of A = {1, 2, 3}.
  Number of elements = 2^3 = 8
• 15. If A = {1, 2, 3} and B = {4, 5, 6}, find A × B.
  A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}
• 16. If A = {x | x is a natural number and x < 5} and B = {3, 4, 5}, find A ∩ B.
  A ∩ B = {3, 4}
• 17. Find the union of A = {1, 3, 5} and B = {2, 4, 6}.
  A ∪ B = {1, 2, 3, 4, 5, 6}
• 18. If A = {1, 2, 3} and B = {3, 4, 5}, find A - B and B - A.
  A - B = {1, 2}; B - A = {4, 5}
• 19. Determine if {a, b} is a subset of {a, b, c, d}.
  Yes, {a, b} ⊆ {a, b, c, d}
• 20. Find the complement of A = {1, 2, 3} in the universal set U = {1, 2, 3, 4, 5, 6}.
  A' = {4, 5, 6}
• 21. If A = {1, 2, 3} and B = {2, 3, 4, 5}, find A ∪ B and A ∩ B.
  A ∪ B = {1, 2, 3, 4, 5}; A ∩ B = {2, 3}
• 22. Given A = {1, 2, 3, 4} and B = {2, 4, 6}, find the difference A - B.
  A - B = {1, 3}
• 23. Find the number of elements in the set of all subsets of A = {a, b}.
  Number of subsets = 2^2 = 4
• 24. If A = {x | x is a positive integer less than 6} and B = {4, 5, 6}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5, 6}
• 25. Find A × B where A = {1, 2} and B = {x | x is a vowel in the English alphabet}.
  A × B = {(1, a), (1, e), (1, i), (1, o), (1, u), (2, a), (2, e), (2, i), (2, o), (2, u)}
• 26. If A = {1, 2, 3} and B = {2, 3, 4}, find A ∪ B and A ∩ B.
  A ∪ B = {1, 2, 3, 4}; A ∩ B = {2, 3}
• 27. Find the power set of A = {x | x is a digit less than 3}.
  Power set = {∅, {0}, {1}, {0, 1}}
• 28. If A = {2, 4, 6, 8} and B = {1, 2, 3, 4}, find A ∩ B and A - B.
  A ∩ B = {2, 4}; A - B = {6, 8}
• 29. Given A = {x | x is a positive even number less than 10} and B = {2, 4, 6}, find the symmetric difference of A and B.
  A Δ B = ∅
• 30. Determine if the set {x | x is a negative integer} is a subset of {x | x is an integer}.
  Yes, {x | x is a negative integer} ⊆ {x | x is an integer}
• 31. Find the intersection of A = {x, y, z} and B = {y, z, w}.
  A ∩ B = {y, z}
• 32. Determine if {1, 2} is a subset of {1, 2, 3, 4}.
  Yes, {1, 2} ⊆ {1, 2, 3, 4}
• 33. Find the power set of A = {1, 2}.
  Power set = {∅, {1}, {2}, {1, 2}}
• 34. If A = {2, 4, 6} and B = {4, 6, 8}, find A - B.
  A - B = {2}
• 35. Find the symmetric difference of A = {1, 2, 3} and B = {2, 3, 4}.
  A Δ B = {1, 4}
• 36. If A = {a, b, c} and B = {b, c, d}, find the Cartesian product A × B.
  A × B = {(a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, b), (c, c), (c, d)}
• 37. Determine if {1, 2, 3} is a proper subset of {1, 2, 3, 4}.
  Yes, {1, 2, 3} ⊂ {1, 2, 3, 4}
• 38. Find the power set of B = {a, b}.
  Power set = {∅, {a}, {b}, {a, b}}
• 39. If A = {1, 2, 3} and B = {2, 3, 4}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4}
• 40. Find the intersection of A = {a, b, c} and B = {b, c, d, e}.
  A ∩ B = {b, c}
• 41. Determine if {a, b} is a subset of {a, b, c, d}.
  Yes, {a, b} ⊆ {a, b, c, d}
• 42. Find the Cartesian product of A = {1, 2} and B = {a, b}.
  A × B = {(1, a), (1, b), (2, a), (2, b)}
• 43. If A = {x | x is an even number} and B = {2, 4, 6}, find A ∩ B.
  A ∩ B = {2, 4, 6}
• 44. Find the union of A = {2, 4} and B = {1, 3, 5}.
  A ∪ B = {1, 2, 3, 4, 5}
• 45. If A = {2, 4, 6} and B = {4, 8, 10}, find A Δ B.
  A Δ B = {2, 6, 8, 10}
• 46. Determine if {1, 2} is a proper subset of {1, 2, 3, 4}.
  Yes, {1, 2} ⊂ {1, 2, 3, 4}
• 47. Find the power set of A = {a}.
  Power set = {∅, {a}}
• 48. If A = {1, 3, 5} and B = {3, 5, 7}, find A ∩ B.
  A ∩ B = {3, 5}
• 49. Find the symmetric difference of A = {a, b} and B = {b, c}.
  A Δ B = {a, c}
• 50. If A = {a, b, c} and B = {c, d, e}, find A - B.
  A - B = {a, b}

Questions 51 to 100

• 51. If A = {x | x is a multiple of 3} and B = {x | x is a multiple of 4}, find A ∩ B.
  A ∩ B = {x | x is a multiple of 12}
• 52. Find the number of elements in the power set of B = {2, 4, 6}.
  Number of elements = 2^3 = 8
• 53. If A = {1, 2, 3} and B = {2, 3, 4}, find the Cartesian product A × B.
  A × B = {(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}
• 54. Find the union of A = {a, b, c} and B = {b, c, d, e}.
  A ∪ B = {a, b, c, d, e}
• 55. If A = {1, 2, 3} and B = {2, 3, 4, 5}, find |A ∩ B|.
  |A ∩ B| = 2
• 56. If U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, find the complement of A.
  A' = {1, 3, 5}
• 57. Determine if {a, b} is a subset of {a, b, c}.
  Yes, {a, b} ⊆ {a, b, c}
• 58. Find the symmetric difference of A = {1, 2, 3} and B = {3, 4, 5}.
  A Δ B = {1, 2, 4, 5}
• 59. If A = {1, 3, 5} and B = {2, 4, 6}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5, 6}
• 60. Given A = {1, 2} and B = {2, 3, 4}, find A ∪ B and A ∩ B.
  A ∪ B = {1, 2, 3, 4}; A ∩ B = {2}
• 61. If A = {2, 4, 6} and B = {1, 2, 3}, find A - B and B - A.
  A - B = {4, 6}; B - A = {1, 3}
• 62. Find the number of elements in the set of all subsets of A = {x | x is a digit}.
  Number of elements = 2^10 = 1024
• 63. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A Δ B.
  A Δ B = {1, 2, 5, 6}
• 64. If U = {1, 2, 3, 4, 5} and A = {2, 3}, find the difference U - A.
  U - A = {1, 4, 5}
• 65. Determine if the set {1, 2} is a proper subset of {1, 2, 3}.
  Yes, {1, 2} ⊂ {1, 2, 3}
• 66. Find the power set of A = {1, 2}.
  Power set = {∅, {1}, {2}, {1, 2}}
• 67. If A = {a, b} and B = {b, c}, find A ∪ B.
  A ∪ B = {a, b, c}
• 68. If A = {1, 2, 3} and B = {3, 4, 5}, find A ∩ B.
  A ∩ B = {3}
• 69. Find the union of A = {1, 3, 5} and B = {3, 4, 6}.
  A ∪ B = {1, 3, 4, 5, 6}
• 70. If A = {1, 2} and B = {2, 3, 4}, find A ∩ B and A - B.
  A ∩ B = {2}; A - B = {1}
• 71. Given A = {2, 4, 6} and B = {2, 3, 6}, find A Δ B.
  A Δ B = {3, 4}
• 72. Find the number of elements in the set of all subsets of A = {1, 2, 3}.
  Number of elements = 2^3 = 8
• 73. If A = {x | x is an even number less than 10} and B = {x | x is a positive integer less than 10}, find A ∩ B.
  A ∩ B = {2, 4, 6, 8}
• 74. Determine if the set {2, 4, 6} is a subset of {1, 2, 3, 4, 5, 6}.
  Yes, {2, 4, 6} ⊆ {1, 2, 3, 4, 5, 6}
• 75. If U = {1, 2, 3, 4, 5} and A = {2, 4}, find the complement of A.
  A' = {1, 3, 5}
• 76. Find the power set of A = {1, 3}.
  Power set = {∅, {1}, {3}, {1, 3}}
• 77. If A = {1, 2, 3} and B = {2, 4, 6}, find A - B.
  A - B = {1, 3}
• 78. If A = {1, 2} and B = {1, 2, 3}, find A ∪ B.
  A ∪ B = {1, 2, 3}
• 79. Find the intersection of A = {1, 2, 3} and B = {2, 3, 4}.
  A ∩ B = {2, 3}
• 80. If A = {2, 4, 6, 8} and B = {1, 3, 5, 7}, find A ∩ B.
  A ∩ B = ∅
• 81. If A = {a, b, c} and B = {b, c, d}, find A ∪ B.
  A ∪ B = {a, b, c, d}
• 82. Find the number of elements in the power set of B = {1, 2, 3, 4}.
  Number of elements = 2^4 = 16
• 83. If A = {2, 4, 6} and B = {4, 5, 6}, find the union A ∪ B.
  A ∪ B = {2, 4, 5, 6}
• 84. Determine if {1, 2} is a subset of {1, 2, 3}.
  Yes, {1, 2} ⊆ {1, 2, 3}
• 85. If A = {a, b} and B = {a, b, c}, find A - B.
  A - B = ∅
• 86. Find the symmetric difference of A = {1, 2, 3} and B = {2, 3, 4}.
  A Δ B = {1, 4}
• 87. If A = {1, 2, 3} and B = {2, 3, 4}, find the Cartesian product A × B.
  A × B = {(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}
• 88. Given A = {2, 4, 6} and B = {1, 2, 3, 4}, find the intersection A ∩ B.
  A ∩ B = {2, 4}
• 89. Find the number of elements in the set of all subsets of A = {1, 2}.
  Number of elements = 2^2 = 4
• 90. If A = {a, b, c} and B = {b, c, d}, find A Δ B.
  A Δ B = {a, d}
• 91. If A = {1, 3, 5} and B = {2, 4, 6}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5, 6}
• 92. Determine if {2, 4, 6} is a subset of {1, 2, 3, 4, 5, 6}.
  Yes, {2, 4, 6} ⊆ {1, 2, 3, 4, 5, 6}
• 93. Find the power set of A = {a}.
  Power set = {∅, {a}}
• 94. If A = {1, 2, 3} and B = {2, 4, 6}, find A ∩ B.
  A ∩ B = {2}
• 95. Find the union of A = {1, 3, 5} and B = {3, 6, 9}.
  A ∪ B = {1, 3, 5, 6, 9}
• 96. If A = {a, b, c} and B = {b, c, d, e}, find A - B.
  A - B = {a}
• 97. Find the symmetric difference of A = {1, 2, 3} and B = {3, 4, 5}.
  A Δ B = {1, 2, 4, 5}
• 98. If A = {1, 2, 3} and B = {2, 3, 4}, find A - B and B - A.
  A - B = {1}; B - A = {4}
• 99. Determine if {1, 2} is a proper subset of {1, 2, 3}.
  Yes, {1, 2} ⊂ {1, 2, 3}
• 100. Find the number of elements in the set of all subsets of A = {x | x is an odd digit}.
  Number of elements = 2^5 = 32

Questions 101 to 150

• 101. If A = {1, 2, 3} and B = {2, 3, 4}, find A × B.
  A × B = {(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}
• 102. Find the number of elements in the power set of A = {a, b}.
  Number of elements = 2^2 = 4
• 103. If A = {1, 2, 3, 4} and B = {2, 4, 6, 8}, find A ∩ B.
  A ∩ B = {2, 4}
• 104. Determine if A = {x | x is a positive integer less than 5} is a subset of B = {1, 2, 3, 4}.
  Yes, A ⊆ B
• 105. Find the symmetric difference of A = {1, 2, 3} and B = {3, 4, 5}.
  A Δ B = {1, 2, 4, 5}
• 106. If A = {1, 2, 3} and B = {2, 3, 4}, find the Cartesian product A × B.
  A × B = {(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}
• 107. Find the union of A = {a, b} and B = {b, c, d}.
  A ∪ B = {a, b, c, d}
• 108. If A = {2, 4, 6} and B = {1, 3, 5}, find A - B.
  A - B = {2, 4, 6}
• 109. Find the complement of A = {2, 4, 6} in the universal set U = {1, 2, 3, 4, 5, 6}.
  A' = {1, 3, 5}
• 110. Determine if {a, b} is a subset of {a, b, c, d}.
  Yes, {a, b} ⊆ {a, b, c, d}
• 111. Find the number of elements in the set of all subsets of A = {1, 2, 3, 4}.
  Number of elements = 2^4 = 16
• 112. If A = {a, b, c} and B = {b, c, d}, find A Δ B.
  A Δ B = {a, d}
• 113. Given A = {1, 2, 3} and B = {2, 4, 6}, find A ∩ B.
  A ∩ B = {2}
• 114. Find the power set of A = {1}.
  Power set = {∅, {1}}
• 115. If A = {a, b, c} and B = {a, b, c, d}, find A - B.
  A - B = ∅
• 116. Find the union of A = {x | x is an even number} and B = {x | x is a multiple of 3}.
  A ∪ B = {x | x is an even number or a multiple of 3}
• 117. Determine if {1, 2, 3} is a proper subset of {1, 2, 3, 4, 5}.
  Yes, {1, 2, 3} ⊂ {1, 2, 3, 4, 5}
• 118. Find the number of elements in the power set of B = {2, 4, 6}.
  Number of elements = 2^3 = 8
• 119. If A = {1, 3, 5} and B = {2, 4, 6}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5, 6}
• 120. If A = {a, b} and B = {b, c}, find A ∩ B.
  A ∩ B = {b}
• 121. Find the symmetric difference of A = {1, 2, 3, 4} and B = {3, 4, 5, 6}.
  A Δ B = {1, 2, 5, 6}
• 122. If A = {x | x is a natural number less than 10} and B = {5, 6, 7, 8, 9}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9}
• 123. Determine if {2, 4} is a subset of {1, 2, 3, 4, 5, 6}.
  Yes, {2, 4} ⊆ {1, 2, 3, 4, 5, 6}
• 124. Find the power set of A = {2, 3}.
  Power set = {∅, {2}, {3}, {2, 3}}
• 125. If A = {1, 2, 3} and B = {2, 3, 4}, find A - B.
  A - B = {1}
• 126. Find the intersection of A = {a, b, c} and B = {b, c, d}.
  A ∩ B = {b, c}
• 127. Determine if {1, 3} is a proper subset of {1, 2, 3, 4}.
  Yes, {1, 3} ⊂ {1, 2, 3, 4}
• 128. Find the number of elements in the power set of A = {1, 2, 3, 4}.
  Number of elements = 2^4 = 16
• 129. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find the union A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5, 6}
• 130. Find the symmetric difference of A = {a, b, c} and B = {b, c, d}.
  A Δ B = {a, d}
• 131. If A = {1, 2, 3} and B = {2, 3, 4}, find the Cartesian product A × B.
  A × B = {(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}
• 132. Determine if {2, 4} is a subset of {1, 2, 3, 4, 5}.
  Yes, {2, 4} ⊆ {1, 2, 3, 4, 5}
• 133. Find the power set of A = {a}.
  Power set = {∅, {a}}
• 134. If A = {1, 2, 3, 4} and B = {1, 2}, find A - B.
  A - B = {3, 4}
• 135. Find the union of A = {1, 2, 3} and B = {3, 4, 5}.
  A ∪ B = {1, 2, 3, 4, 5}
• 136. If A = {a, b, c} and B = {b, c, d, e}, find A ∩ B.
  A ∩ B = {b, c}
• 137. Determine if {1, 2, 3} is a proper subset of {1, 2, 3, 4, 5}.
  Yes, {1, 2, 3} ⊂ {1, 2, 3, 4, 5}
• 138. Find the symmetric difference of A = {2, 4, 6} and B = {4, 6, 8}.
  A Δ B = {2, 8}
• 139. If A = {x | x is a positive integer less than 6} and B = {4, 5, 6}, find A ∩ B.
  A ∩ B = {4, 5}
• 140. Find the number of elements in the set of all subsets of A = {1, 2, 3}.
  Number of elements = 2^3 = 8
• 141. If A = {x | x is an even number} and B = {x | x is a positive integer}, find A ∪ B.
  A ∪ B = {x | x is an even number or a positive integer}
• 142. Determine if {3, 4, 5} is a subset of {2, 3, 4, 5, 6}.
  Yes, {3, 4, 5} ⊆ {2, 3, 4, 5, 6}
• 143. Find the power set of A = {x | x is a prime number less than 5}.
  Power set = {∅, {2}, {3}, {2, 3}}
• 144. If A = {1, 2, 3, 4, 5} and B = {1, 2, 3}, find A - B.
  A - B = {4, 5}
• 145. Find the intersection of A = {a, b, c, d} and B = {b, c, e, f}.
  A ∩ B = {b, c}
• 146. Determine if {a, b} is a subset of {a, b, c, d, e}.
  Yes, {a, b} ⊆ {a, b, c, d, e}
• 147. Find the number of elements in the power set of B = {x | x is a digit from 0 to 3}.
  Number of elements = 2^4 = 16
• 148. If A = {2, 4, 6} and B = {4, 6, 8, 10}, find A ∪ B.
  A ∪ B = {2, 4, 6, 8, 10}
• 149. Find the symmetric difference of A = {1, 2, 3, 4} and B = {3, 4, 5, 6}.
  A Δ B = {1, 2, 5, 6}
• 150. If A = {a, b, c} and B = {c, d, e}, find the union A ∪ B.
  A ∪ B = {a, b, c, d, e}

Questions 151 to 200

• 151. Determine if {2, 4, 6} is a proper subset of {1, 2, 3, 4, 5, 6}.
  Yes, {2, 4, 6} ⊂ {1, 2, 3, 4, 5, 6}
• 152. Find the number of elements in the power set of A = {1, 2}.
  Number of elements = 2^2 = 4
• 153. If A = {1, 2, 3} and B = {2, 3, 4}, find A Δ B.
  A Δ B = {1, 4}
• 154. Find the Cartesian product of A = {1, 2} and B = {a, b}.
  A × B = {(1, a), (1, b), (2, a), (2, b)}
• 155. If A = {x | x is a natural number less than 8} and B = {5, 6, 7}, find A ∩ B.
  A ∩ B = {5, 6, 7}
• 156. Find the union of A = {1, 3, 5} and B = {2, 4, 6}.
  A ∪ B = {1, 2, 3, 4, 5, 6}
• 157. If A = {x | x is a prime number less than 10} and B = {2, 3, 5}, find A ∪ B.
  A ∪ B = {2, 3, 5, 7}
• 158. Determine if {1, 3, 5} is a subset of {1, 2, 3, 4, 5, 6}.
  Yes, {1, 3, 5} ⊆ {1, 2, 3, 4, 5, 6}
• 159. Find the power set of A = {a, b}.
  Power set = {∅, {a}, {b}, {a, b}}
• 160. If A = {2, 4, 6} and B = {1, 2, 3}, find A - B.
  A - B = {4, 6}
• 161. Find the intersection of A = {1, 2, 3} and B = {2, 3, 4}.
  A ∩ B = {2, 3}
• 162. Determine if {a, b, c} is a proper subset of {a, b, c, d, e}.
  Yes, {a, b, c} ⊂ {a, b, c, d, e}
• 163. Find the symmetric difference of A = {1, 2, 3} and B = {2, 3, 4, 5}.
  A Δ B = {1, 4, 5}
• 164. If A = {1, 2, 3, 4} and B = {2, 3, 5, 6}, find the union A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5, 6}
• 165. Find the Cartesian product of A = {x, y} and B = {1, 2}.
  A × B = {(x, 1), (x, 2), (y, 1), (y, 2)}
• 166. If A = {a, b, c, d} and B = {c, d, e, f}, find A - B.
  A - B = {a, b}
• 167. Determine if {1, 2, 3, 4} is a subset of {1, 2, 3, 4, 5, 6}.
  Yes, {1, 2, 3, 4} ⊆ {1, 2, 3, 4, 5, 6}
• 168. Find the power set of B = {1, 2, 3}.
  Power set = {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
• 169. If A = {x | x is an odd number less than 10} and B = {1, 3, 5, 7}, find A ∪ B.
  A ∪ B = {1, 3, 5, 7, 9}
• 170. Find the intersection of A = {a, b, c} and B = {b, c, d, e}.
  A ∩ B = {b, c}
• 171. Determine if {1, 2} is a proper subset of {1, 2, 3, 4}.
  Yes, {1, 2} ⊂ {1, 2, 3, 4}
• 172. Find the number of elements in the set of all subsets of A = {1, 2, 3, 4, 5}.
  Number of elements = 2^5 = 32
• 173. If A = {x | x is a natural number} and B = {2, 4, 6}, find A ∩ B.
  A ∩ B = {2, 4, 6}
• 174. Find the union of A = {1, 3, 5} and B = {3, 5, 7}.
  A ∪ B = {1, 3, 5, 7}
• 175. If A = {2, 4, 6} and B = {2, 4, 8}, find A Δ B.
  A Δ B = {6, 8}
• 176. Determine if {a, b} is a subset of {a, b, c, d, e}.
  Yes, {a, b} ⊆ {a, b, c, d, e}
• 177. Find the power set of A = {1, 2, 3, 4}.
  Power set = {∅, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
• 178. If A = {a, b, c} and B = {c, d, e}, find the Cartesian product A × B.
  A × B = {(a, c), (a, d), (a, e), (b, c), (b, d), (b, e), (c, c), (c, d), (c, e)}
• 179. Find the intersection of A = {2, 4, 6} and B = {4, 6, 8}.
  A ∩ B = {4, 6}
• 180. Determine if {x, y} is a proper subset of {x, y, z, w}.
  Yes, {x, y} ⊂ {x, y, z, w}
• 181. Find the number of elements in the power set of A = {a, b, c}.
  Number of elements = 2^3 = 8
• 182. If A = {1, 2, 3} and B = {1, 3, 4, 5}, find A ∩ B.
  A ∩ B = {1, 3}
• 183. Find the union of A = {a, b} and B = {b, c}.
  A ∪ B = {a, b, c}
• 184. If A = {a, b} and B = {b, c, d}, find A - B.
  A - B = {a}
• 185. Find the Cartesian product of A = {1, 2} and B = {a, b, c}.
  A × B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)}
• 186. Determine if {2, 4} is a proper subset of {2, 4, 6, 8}.
  Yes, {2, 4} ⊂ {2, 4, 6, 8}
• 187. Find the power set of B = {a, b, c}.
  Power set = {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
• 188. If A = {1, 2, 3, 4, 5} and B = {1, 3, 5}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5}
• 189. Find the symmetric difference of A = {1, 2, 3} and B = {2, 3, 4}.
  A Δ B = {1, 4}
• 190. Determine if {a, b} is a subset of {a, b, c}.
  Yes, {a, b} ⊆ {a, b, c}
• 191. Find the intersection of A = {x, y} and B = {y, z}.
  A ∩ B = {y}
• 192. If A = {1, 2, 3} and B = {2, 3, 4}, find A - B.
  A - B = {1}
• 193. Find the number of elements in the power set of A = {a, b, c, d}.
  Number of elements = 2^4 = 16
• 194. If A = {a, b, c} and B = {b, c, d, e}, find A ∪ B.
  A ∪ B = {a, b, c, d, e}
• 195. Determine if {1, 2, 3} is a proper subset of {1, 2, 3, 4}.
  Yes, {1, 2, 3} ⊂ {1, 2, 3, 4}
• 196. Find the symmetric difference of A = {a, b, c} and B = {b, c, d}.
  A Δ B = {a, d}
• 197. If A = {1, 2, 3} and B = {3, 4, 5}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5}
• 198. Find the Cartesian product of A = {1, 2} and B = {x, y, z}.
  A × B = {(1, x), (1, y), (1, z), (2, x), (2, y), (2, z)}
• 199. Determine if {a, b, c} is a proper subset of {a, b, c, d, e}.
  Yes, {a, b, c} ⊂ {a, b, c, d, e}
• 200. Find the power set of A = {1, 2, 3}.
  Power set = {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
• 200. Find the power set of A = {1, 2, 3}.
  Power set = {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
• 201. If A = {1, 2, 3, 4, 5} and B = {2, 4, 6}, find A - B.
  A - B = {1, 3, 5}
• 202. Find the symmetric difference of A = {1, 2, 3} and B = {2, 3, 4, 5}.
  A Δ B = {1, 4, 5}
• 203. Determine if {a, b} is a subset of {a, b, c, d}.
  Yes, {a, b} ⊆ {a, b, c, d}
• 204. Find the power set of B = {x, y}.
  Power set = {∅, {x}, {y}, {x, y}}
• 205. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A ∩ B.
  A ∩ B = {3, 4}
• 206. Find the union of A = {1, 2, 3} and B = {2, 3, 4, 5}.
  A ∪ B = {1, 2, 3, 4, 5}
• 207. If A = {a, b, c} and B = {b, c, d}, find the Cartesian product A × B.
  A × B = {(a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, b), (c, c), (c, d)}
• 208. Determine if {1, 2} is a proper subset of {1, 2, 3, 4}.
  Yes, {1, 2} ⊂ {1, 2, 3, 4}
• 209. Find the power set of A = {a, b}.
  Power set = {∅, {a}, {b}, {a, b}}
• 210. If A = {1, 2, 3, 4} and B = {2, 3}, find A - B.
  A - B = {1, 4}
• 211. Find the symmetric difference of A = {1, 2, 3} and B = {2, 3, 4}.
  A Δ B = {1, 4}
• 212. If A = {a, b} and B = {b, c, d}, find A - B.
  A - B = {a}
• 213. Determine if {x, y} is a proper subset of {x, y, z, w}.
  Yes, {x, y} ⊂ {x, y, z, w}
• 214. Find the power set of B = {1, 2, 3}.
  Power set = {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
• 215. If A = {a, b, c} and B = {c, d, e}, find A ∩ B.
  A ∩ B = {c}
• 216. Find the union of A = {x, y} and B = {y, z, w}.
  A ∪ B = {x, y, z, w}
• 217. Determine if {1, 2} is a subset of {1, 2, 3, 4, 5}.
  Yes, {1, 2} ⊆ {1, 2, 3, 4, 5}
• 218. Find the Cartesian product of A = {x} and B = {1, 2}.
  A × B = {(x, 1), (x, 2)}
• 219. If A = {a, b, c} and B = {b, c, d, e}, find A - B.
  A - B = {a}
• 220. Find the power set of A = {1, 2, 3}.
  Power set = {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
• 221. Determine if {a, b} is a proper subset of {a, b, c}.
  Yes, {a, b} ⊂ {a, b, c}
• 222. Find the intersection of A = {1, 3, 5} and B = {3, 5, 7, 9}.
  A ∩ B = {3, 5}
• 223. Find the symmetric difference of A = {a, b, c} and B = {b, c, d}.
  A Δ B = {a, d}
• 224. If A = {1, 2, 3} and B = {2, 3, 4, 5}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4, 5}
• 225. Find the power set of B = {a, b}.
  Power set = {∅, {a}, {b}, {a, b}}
• 226. If A = {2, 4, 6} and B = {1, 2, 3}, find A - B.
  A - B = {4, 6}
• 227. Find the Cartesian product of A = {1, 2} and B = {x, y}.
  A × B = {(1, x), (1, y), (2, x), (2, y)}
• 228. Determine if {x, y} is a proper subset of {x, y, z}.
  Yes, {x, y} ⊂ {x, y, z}
• 229. Find the power set of A = {1, 2, 3, 4}.
  Power set = {∅, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
• 230. If A = {a, b, c} and B = {b, c, d}, find the intersection A ∩ B.
  A ∩ B = {b, c}
• 231. Find the symmetric difference of A = {1, 2, 3, 4} and B = {3, 4, 5, 6}.
  A Δ B = {1, 2, 5, 6}
• 232. Determine if {a, b} is a subset of {a, b, c, d, e}.
  Yes, {a, b} ⊆ {a, b, c, d, e}
• 233. Find the power set of A = {1, 2}.
  Power set = {∅, {1}, {2}, {1, 2}}
• 234. If A = {1, 2, 3} and B = {2, 4, 6}, find A ∪ B.
  A ∪ B = {1, 2, 3, 4, 6}
• 235. Find the Cartesian product of A = {1, 2} and B = {a, b, c}.
  A × B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)}
• 236. Determine if {2, 4, 6} is a proper subset of {2, 4, 6, 8}.
  Yes, {2, 4, 6} ⊂ {2, 4, 6, 8}
• 237. Find the symmetric difference of A = {1, 3, 5} and B = {2, 3, 4, 5}.
  A Δ B = {1, 2, 4}
• 238. If A = {a, b} and B = {a, b, c, d, e}, find A - B.
  A - B = ∅
• 239. Find the power set of B = {a, b, c}.
  Power set = {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
• 240. If A = {x, y, z} and B = {y, z, w}, find A ∩ B.
  A ∩ B = {y, z}
• 241. Find the union of A = {1, 2, 3} and B = {3, 4, 5}.
  A ∪ B = {1, 2, 3, 4, 5}
• 242. Determine if {a, b, c} is a proper subset of {a, b, c, d}.
  Yes, {a, b, c} ⊂ {a, b, c, d}
• 243. Find the Cartesian product of A = {a, b} and B = {1, 2}.
  A × B = {(a, 1), (a, 2), (b, 1), (b, 2)}
• 244. If A = {2, 4, 6} and B = {1, 2, 3}, find A - B.
  A - B = {4, 6}
• 245. Find the symmetric difference of A = {1, 2} and B = {2, 3}.
  A Δ B = {1, 3}
• 246. If A = {x, y} and B = {y, z, w}, find A - B.
  A - B = {x}
• 247. Find the power set of A = {1, 2, 3, 4, 5}.
  Power set = {∅, {1}, {2}, {3}, {4}, {5}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}, {3, 5}, {4, 5}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5}, {1, 4, 5}, {2, 3, 4}, {2, 3, 5}, {2, 4, 5}, {3, 4, 5}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {1, 3, 4, 5}, {2, 3, 4, 5}, {1, 2, 3, 4, 5}}
• 248. Determine if {a, b, c} is a subset of {a, b, c, d, e}.
  Yes, {a, b, c} ⊆ {a, b, c, d, e}
• 249. Find the intersection of A = {1, 2, 3, 4} and B = {3, 4, 5, 6}.
  A ∩ B = {3, 4}
• 250. Find the symmetric difference of A = {a, b} and B = {b, c, d}.
  A Δ B = {a, c, d}
• 251. If A = {1, 2, 3, 4, 5} and B = {1, 3, 5}, find A - B.
  A - B = {2, 4}
• 252. Find the power set of B = {x, y, z}.
  Power set = {∅, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}
• 253. Determine if {1, 2} is a proper subset of {1, 2, 3, 4}.
  Yes, {1, 2} ⊂ {1, 2, 3, 4}
• 254. Find the Cartesian product of A = {a} and B = {1, 2, 3}.
  A × B = {(a, 1), (a, 2), (a, 3)}
• 255. If A = {x, y} and B = {x, y, z, w}, find A ∪ B.
  A ∪ B = {x, y, z, w}
• 256. Find the symmetric difference of A = {2, 4, 6} and B = {4, 6, 8}.
  A Δ B = {2, 8}
• 257. Determine if {a, b, c} is a subset of {a, b, c, d}.
  Yes, {a, b, c} ⊆ {a, b, c, d}
• 258. Find the power set of A = {1, 2, 3, 4}.
  Power set = {∅, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
• 259. If A = {a, b} and B = {b, c}, find A ∩ B.
  A ∩ B = {b}
• 260. Find the union of A = {1, 2} and B = {2, 3, 4}.
  A ∪ B = {1, 2, 3, 4}
• 261. Determine if {x, y} is a proper subset of {x, y, z, w}.
  Yes, {x, y} ⊂ {x, y, z, w}
• 262. Find the Cartesian product of A = {1} and B = {a, b, c}.
  A × B = {(1, a), (1, b), (1, c)}
• 263. If A = {1, 2, 3} and B = {2, 4}, find A - B.
  A - B = {1, 3}
• 264. Find the symmetric difference of A = {1, 2, 3} and B = {2, 3, 4, 5}.
  A Δ B = {1, 4, 5}
• 265. Determine if {1, 2, 3} is a subset of {1, 2, 3, 4, 5}.
  Yes, {1, 2, 3} ⊆ {1, 2, 3, 4, 5}
• 266. Find the power set of B = {x, y, z, w}.
  Power set = {∅, {x}, {y}, {z}, {w}, {x, y}, {x, z}, {x, w}, {y, z}, {y, w}, {z, w}, {x, y, z}, {x, y, w}, {x, z, w}, {y, z, w}, {x, y, z, w}}
• 267. If A = {a, b} and B = {a, b, c, d}, find A ∪ B.
  A ∪ B = {a, b, c, d}
• 268. Find the Cartesian product of A = {1, 2} and B = {a, b}.
  A × B = {(1, a), (1, b), (2, a), (2, b)}
• 269. Determine if {1, 2} is a proper subset of {1, 2, 3}.
  Yes, {1, 2} ⊂ {1, 2, 3}
• 270. Find the power set of A = {1, 2}.
  Power set = {∅, {1}, {2}, {1, 2}}
• 271. If A = {a, b, c} and B = {c, d, e}, find A ∩ B.
  A ∩ B = {c}
• 272. Find the symmetric difference of A = {1, 2} and B = {2, 3}.
  A Δ B = {1, 3}
• 273. Determine if {a, b, c} is a subset of {a, b, c, d}.
  Yes, {a, b, c} ⊆ {a, b, c, d}
• 274. Find the Cartesian product of A = {x} and B = {1, 2}.
  A × B = {(x, 1), (x, 2)}
• 275. If A = {1, 3, 5} and B = {2, 3, 4}, find A - B.
  A - B = {1, 5}
• 276. Find the power set of B = {1, 2, 3}.
  Power set = {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
• 277. Determine if {1, 2, 3} is a proper subset of {1, 2, 3, 4}.
  Yes, {1, 2, 3} ⊂ {1, 2, 3, 4}
• 278. Find the symmetric difference of A = {a, b, c} and B = {b, c, d}.
  A Δ B = {a, d}
• 279. If A = {1, 2} and B = {2, 3}, find A ∪ B.
  A ∪ B = {1, 2, 3}
• 280. Find the Cartesian product of A = {a, b} and B = {1, 2}.
  A × B = {(a, 1), (a, 2), (b, 1), (b, 2)}
• 281. Determine if {1, 2} is a subset of {1, 2, 3, 4}.
  Yes, {1, 2} ⊆ {1, 2, 3, 4}
• 282. Find the power set of A = {a, b, c}.
  Power set = {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
• 283. Find the union of A = {1, 2} and B = {2, 4}.
  A ∪ B = {1, 2, 4}
• 284. Determine if {x, y, z} is a subset of {x, y}.
  No, {x, y, z} ⊈ {x, y}
• 285. Find the Cartesian product of A = {1, 2} and B = {2, 3}.
  A × B = {(1, 2), (1, 3), (2, 2), (2, 3)}
• 286. If A = {1, 2} and B = {2, 3, 4}, find A - B.
  A - B = ∅
• 287. Find the symmetric difference of A = {a, b} and B = {b, c}.
  A Δ B = {a, c}
• 288. Determine if {1, 2, 3} is a proper subset of {1, 2, 3, 4, 5}.
  Yes, {1, 2, 3} ⊂ {1, 2, 3, 4, 5}
• 289. Find the power set of B = {a, b, c, d}.
  Power set = {∅, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}, {a, b, c, d}}
• 290. If A = {x, y, z} and B = {x, y}, find A - B.
  A - B = {z}
• 291. Find the union of A = {1, 2, 3} and B = {2, 3, 4}.
  A ∪ B = {1, 2, 3, 4}
• 292. Determine if {a, b} is a proper subset of {a, b, c}.
  Yes, {a, b} ⊂ {a, b, c}
• 293. Find the Cartesian product of A = {1, 2} and B = {a, b, c, d}.
  A × B = {(1, a), (1, b), (1, c), (1, d), (2, a), (2, b), (2, c), (2, d)}
• 294. Find the symmetric difference of A = {1, 2} and B = {2, 3, 4}.
  A Δ B = {1, 3, 4}
• 295. Determine if {x, y, z} is a subset of {x, y, z, w}.
  Yes, {x, y, z} ⊆ {x, y, z, w}
• 296. Find the power set of A = {x, y, z}.
  Power set = {∅, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}
• 297. If A = {1, 3} and B = {2, 3, 4}, find A - B.
  A - B = {1}
• 298. Find the union of A = {1, 2} and B = {1, 3, 4}.
  A ∪ B = {1, 2, 3, 4}
• 299. Determine if {a, b, c} is a subset of {a, b}.
  No, {a, b, c} ⊈ {a, b}
• 300. Find the Cartesian product of A = {1, 2} and B = {2, 4}.
  A × B = {(1, 2), (1, 4), (2, 2), (2, 4)}
• 301. Find the power set of A = {a, b, c, d}.
  Power set = {∅, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}, {a, b, c, d}}
• 302. Find the symmetric difference of A = {a, b, c} and B = {b, c, d}.
  A Δ B = {a, d}
• 303. Determine if {1, 2} is a subset of {1, 2, 3, 4, 5}.
  Yes, {1, 2} ⊆ {1, 2, 3, 4, 5}
• 304. Find the Cartesian product of A = {x} and B = {y, z}.
  A × B = {(x, y), (x, z)}
• 305. Find the union of A = {1, 2} and B = {3, 4}.
  A ∪ B = {1, 2, 3, 4}
• 306. Find the power set of A = {1, 2, 3, 4}.
  Power set = {∅, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
• 307. Determine if {a, b} is a proper subset of {a, b, c}.
  Yes, {a, b} ⊂ {a, b, c}
• 308. Find the Cartesian product of A = {1, 2} and B = {a, b, c, d}.
  A × B = {(1, a), (1, b), (1, c), (1, d), (2, a), (2, b), (2, c), (2, d)}
• 309. Find the symmetric difference of A = {x, y} and B = {y, z}.
  A Δ B = {x, z}
• 310. Determine if {1, 2, 3} is a proper subset of {1, 2, 3, 4}.
  Yes, {1, 2, 3} ⊂ {1, 2, 3, 4}
• 311. Find the power set of A = {x, y, z}.
  Power set = {∅, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}
• 312. If A = {1, 2} and B = {2, 4}, find A ∪ B.
  A ∪ B = {1, 2, 4}
• 313. Find the Cartesian product of A = {a, b, c} and B = {1, 2}.
  A × B = {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)}
• 314. Determine if {a, b, c} is a subset of {a, b}.
  No, {a, b, c} ⊈ {a, b}
• 315. Find the power set of B = {1, 2, 3, 4}.
  Power set = {∅, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
• 316. Find the union of A = {a, b} and B = {b, c, d}.
  A ∪ B = {a, b, c, d}
• 317. Find the Cartesian product of A = {1} and B = {x, y, z}.
  A × B = {(1, x), (1, y), (1, z)}
• 318. Determine if {1, 2} is a proper subset of {1, 2, 3}.
  Yes, {1, 2} ⊂ {1, 2, 3}
• 319. Find the symmetric difference of A = {1, 3, 5} and B = {3, 4, 5}.
  A Δ B = {1, 4}
• 320. Find the power set of A = {1, 2}.
  Power set = {∅, {1}, {2}, {1, 2}}