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
In a survey, n(U) = 120, n(A) = 72, n(B) = 65, and n(A ∩ B) = 38. How many students are only in A?If n(A ∪ B ∪ C) = 100, n(A) = 50, n(B) = 45, n(C) = 40, n(A ∩ B) = 18, n(B ∩ C) = 15, and n(C ∩ A) = 12, what is n(A ∩ B ∩ C)?If n(A)=60, n(B)=55, and n(A∩B)=25, how many elements belong to exactly one set?If n(U) = 100, n(A) = 48, n(B) = 52, and n(A′ ∩ B′) = 18, what is n(A ∩ B)?If n(A Δ B) = 54 and n(A ∩ B) = 19, what is n(A ∪ B)?If n(A − B) = x + 4, n(B − A) = 2x − 1, n(A ∩ B) = x + 3, and n(A ∪ B) = 46, what is the value of x?If 60% of students are in A, 50% are in B, and 25% are in both A and B, what percentage are in exactly one of the two sets?If n(A ∪ B) = 88, n(A ∩ B) = 26, and n(A − B) = 35, what is n(B)?If A ⊆ B, n(A) = 32, n(B) = 57 and n(U) = 90, then what is n(B − A)?If n(A) = 45, n(B) = 52 and n(A ∪ B) = 73, what is n(A △ B), where A △ B = (A − B) ∪ (B − A)?If only A has 12, only B has 15, only C has 18, only A ∩ B has 9, only B ∩ C has 7, only C ∩ A has 6, and A ∩ B ∩ C has 4, what is n(A ∩ (B ∪ C))?Given n(U) = 95, n(A′) = 47, n(B′) = 52, and n(A ∩ B) = 18, what is n(A ∪ B)?If n(U) = 95, n(A') = 47, n(B') = 52, and n(A ∩ B) = 18, choose the correct value of n(A ∪ B).If n(A ∩ B') = 24, n(A' ∩ B) = 31, and n(A ∩ B) = 16, what is n(A ∪ B)?In a survey of 90 people, 52 like tea, 47 like coffee, and 25 like both. How many like neither tea nor coffee?Among 100 students, 40 are only in A, 28 are only in B, and 12 are in both. How many are in at least one set?If A ∩ B ∩ C = ∅, n(A) = 30, n(B) = 34, n(C) = 36, n(A ∩ B) = 8, n(B ∩ C) = 10, and n(C ∩ A) = 6, what is n(A ∪ B ∪ C)?If n(A ∪ B ∪ C) = 118, n(A) = 45, n(B) = 50, n(C) = 55, n(A ∩ B) = 18, n(B ∩ C) = 20, and n(C ∩ A) = 16, what is n(A ∩ B ∩ C)?Let A = {x ∈ N : x ≤ 12}, B be the set of even natural numbers not exceeding 12, and C be the set of multiples of 3 not exceeding 12. What is n(B ∩ C)?Let U = {1, 2, ..., 20}, A be the set of prime numbers in U, and B be the set of odd numbers in U. What is A − B?