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Subjects

Mathematics

Operations on Sets (Union, Intersection, Difference)

समुच्चयों पर संक्रियाएँ (संघ, प्रतिच्छेद और अंतर)

In Class 11 Mathematics, the Sets chapter introduces Operations on Sets (Union, Intersection, Difference). Students learn to combine sets using union, identify common elements through intersection, and find elements belonging to one set but not another using difference. They also apply these operations to subset relations, Venn diagrams, and problems involving the number of elements in sets.

Practice questions

If A = {x : x = 2k, k ∈ Z} and B = {x : x = 3m, m ∈ Z}, then A ∩ B is the set of what?Let A = {x : x is a positive natural number, x ≤ 15, and 2 divides x} and B = {x : x is a positive natural number, x ≤ 15, and 5 divides x}. How many elements are in A ∪ B?If A and B are subsets of a universal set U, then (A \ B) ∪ (A ∩ B) is equal to which set?If A \ B has 5 elements, B \ A has 7 elements, and A ∩ B has 4 elements, what is n(A ∪ B)?Let U be a universal set with n(U) = 60. If n(A) = 32, n(B) = 27, and n(A ∩ B) = 11, what is n((A ∪ B)′), the number of elements in the complement of A ∪ B?If A = {1, 2, 3, 4}, how many subsets B ⊆ A satisfy that A \ B has exactly 2 elements?If A = {x ∈ R : 0 ≤ x ≤ 4} and B = {x ∈ R : x² − 4x + 3 ≤ 0}, what is A ∩ B?If A ∪ B = A ∩ C, which conclusion must be true?If A ∩ B = A \ B, what is the correct conclusion about A?If A \ B = B \ A = {2, 5}, what is the correct conclusion?If A ∩ B = ∅, what is (A ∪ B) \ A?Let N = {1, 2, 3, ...}. If A = {x ∈ N : x ≤ 50 and 4 divides x} and B = {x ∈ N : x ≤ 50 and 6 divides x}, what is n(A ∩ B)?If A = {x : x ∈ ℤ, |x| ≤ 3} and B = {x : x ∈ ℤ, x² − 1 = 0}, what is A \ B?If A = {x ∈ R : x ≤ 0} and B = {x ∈ R : x > 2}, what is A ∩ B?If A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C), which law does this illustrate?If A \ B = C and C ∩ B = ∅, what can be said about C ⊆ A?If A, B, and C are sets and A ∩ B = A ∩ C, which statement is definitely true?If A and B are any two sets, then (A ∪ B) \ (A \ B) is equal to which set?If n(A ∪ B) = 54, n(A \ B) = 17, and n(B \ A) = 21, what is n(A ∩ B)?If A = [−4, 2) ∪ (5, 9] and B = (−1, 6], what is A \ B?