Q.1 If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∪ B?
{1, 2, 3}
{2, 3, 4}
{1, 2, 3, 4}
{1, 4}
Explanation - The union of two sets includes all distinct elements from both sets.
Correct answer is: {1, 2, 3, 4}
Q.2 If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?
{1, 2}
{2, 3}
{3, 4}
{1, 4}
Explanation - The intersection of two sets contains elements common to both sets.
Correct answer is: {2, 3}
Q.3 If U = {1, 2, 3, 4, 5} and A = {1, 2}, what is the complement of A (A')?
{1, 2}
{3, 4, 5}
{2, 3}
{1, 3, 5}
Explanation - The complement of A contains all elements in the universal set not in A.
Correct answer is: {3, 4, 5}
Q.4 If A = {1, 2} and B = {3, 4}, what is A ∩ B?
{1, 2, 3, 4}
{}
{1, 3}
{2, 4}
Explanation - There are no common elements between sets A and B; thus, their intersection is the empty set.
Correct answer is: {}
Q.5 If A = {x | x is an even number ≤ 10}, B = {x | x is a multiple of 3 ≤ 12}, what is A ∩ B?
{2, 4, 6, 8, 10}
{3, 6, 9, 12}
{6}
{2, 4}
Explanation - The intersection contains numbers common to both sets: only 6 is both even ≤10 and multiple of 3 ≤12.
Correct answer is: {6}
Q.6 If A = {1, 2, 3} and B = {2, 3, 4}, what is A - B?
{1}
{4}
{1, 4}
{2, 3}
Explanation - A - B is the set of elements in A that are not in B, which is only 1.
Correct answer is: {1}
Q.7 Which of the following is always true for any set A?
A ∪ A = A
A ∩ A = ∅
A - A = A
A ∩ ∅ = A
Explanation - Union of a set with itself is always the set itself.
Correct answer is: A ∪ A = A
Q.8 If A = {1, 2, 3} and B = {3, 4, 5}, what is (A ∪ B) - (A ∩ B)?
{1, 2, 3, 4, 5}
{3}
{1, 2, 4, 5}
{1, 2, 3}
Explanation - Union minus intersection gives elements that are in either set but not in both.
Correct answer is: {1, 2, 4, 5}
Q.9 If A ⊆ B, which of the following is true?
A ∪ B = B
A ∩ B = A
Both A ∪ B = B and A ∩ B = A
A ∪ B = A
Explanation - If A is a subset of B, their union is B, and intersection is A.
Correct answer is: Both A ∪ B = B and A ∩ B = A
Q.10 If |A| = 5, |B| = 4, and |A ∩ B| = 2, what is |A ∪ B|?
7
9
10
6
Explanation - Use the formula |A ∪ B| = |A| + |B| - |A ∩ B| → 5 + 4 - 2 = 7.
Correct answer is: 7
Q.11 If U = {1, 2, 3, 4, 5, 6} and A = {1, 2, 3}, B = {3, 4, 5}, what is (A ∪ B)'?
{6}
{1, 2, 3, 4, 5}
{3}
{6}
Explanation - Complement of A ∪ B in U includes elements not in A ∪ B, which is only 6.
Correct answer is: {6}
Q.12 If A = {x | x is prime ≤ 10}, B = {x | x is even ≤ 10}, find A ∩ B.
{2}
{2, 3, 5, 7}
{1}
{}
Explanation - 2 is the only even prime number ≤10.
Correct answer is: {2}
Q.13 If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7}, find A ∩ B ∩ C.
{4}
{3, 4}
{4, 5, 6}
{}
Explanation - 4 is the only element common to all three sets.
Correct answer is: {4}
Q.14 If A = {x | x is a multiple of 2 ≤ 10}, B = {x | x is a multiple of 3 ≤ 12}, what is A ∪ B?
{2, 3, 4, 6, 8, 9, 10, 12}
{2, 3, 6}
{2, 4, 6, 8, 10}
{3, 6, 9, 12}
Explanation - Union contains all elements from both sets without repetition.
Correct answer is: {2, 3, 4, 6, 8, 9, 10, 12}
Q.15 Which of the following is not a subset of {1, 2, 3}?
{}
{1}
{1, 2, 3}
{4}
Explanation - 4 is not an element of {1, 2, 3}, so {4} is not a subset.
Correct answer is: {4}
Q.16 If |U| = 10, |A| = 4, and |A'| = ?
4
6
10
14
Explanation - Complement of A has |U| - |A| = 10 - 4 = 6 elements.
Correct answer is: 6
Q.17 If A and B are disjoint sets, which of the following is true?
A ∩ B = ∅
A ∪ B = ∅
A ⊆ B
B ⊆ A
Explanation - Disjoint sets have no elements in common.
Correct answer is: A ∩ B = ∅
Q.18 If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, what is (A - B) ∪ (B - A)?
{1, 2, 3, 4, 5, 6}
{1, 2, 5, 6}
{3, 4}
{}
Explanation - Elements in A or B but not in both form the symmetric difference.
Correct answer is: {1, 2, 5, 6}
Q.19 If A = {x | x is odd ≤ 10}, B = {x | x is prime ≤ 10}, find A ∩ B.
{3, 5, 7}
{2, 3, 5, 7}
{1, 3, 5, 7, 9}
{}
Explanation - Intersection contains numbers that are both odd and prime ≤10.
Correct answer is: {3, 5, 7}
Q.20 If A ∪ B = B, which of the following is true?
A ⊆ B
B ⊆ A
A ∩ B = ∅
A = B
Explanation - If union of A and B is B, all elements of A are already in B.
Correct answer is: A ⊆ B
Q.21 If A = {1, 2, 3, 4}, B = {3, 4, 5}, find |A ∪ B| + |A ∩ B|.
7
8
9
6
Explanation - |A ∪ B| = 5, |A ∩ B| = 2 → sum = 7.
Correct answer is: 7
Q.22 The set {x | x² = 4} is equal to:
{2}
{-2, 2}
{0, 2}
{-2}
Explanation - Both -2 and 2 satisfy x² = 4.
Correct answer is: {-2, 2}
Q.23 If A = {1, 2}, B = {1, 2, 3}, find (B - A) ∩ A.
{1, 2}
{3}
{}
{1}
Explanation - B - A = {3}, intersection with A = {} (empty set).
Correct answer is: {}
Q.24 If a set has 5 elements, how many subsets can it have?
10
16
32
25
Explanation - Number of subsets = 2^n = 2^5 = 32.
Correct answer is: 32