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Class 10 · Mathematics · Hard
→If n(A) = 55, n(B) = 60, n(C) = 65, n(A ∪ B ∪ C) = 120, and n(A ∩ B) + n(B ∩ C) + n(C ∩ A) = 78, what is n(A ∩ B ∩ C)?
Class 12 · Mathematics · Hard
→If n(A ∪ B ∪ C) = 95, exactly one set contains 46 elements, and exactly two sets contain 33 elements, what is n(A ∩ B ∩ C)?
Class 10 · Mathematics · Hard
→In the Venn diagram of A, B, and C, only A ∩ B has 11 elements, only B ∩ C has 13, only C ∩ A has 9, and all three have 4. What is n(A ∩ B) + n(B ∩ C) + n(C ∩ A)?
Class 10 · Mathematics · Medium
→If n(A ∩ B′) = 18, n(A′ ∩ B) = 22, n(A ∩ B) = 16, and n(U) = 75, what is n(A′ ∩ B′)?
Class 10 · Mathematics · Medium
→If n(A ∩ B′) = 29, n(A′ ∩ B) = 34, and n(A ∩ B) = 21, what is n(A ∪ B)?
Class 10 · Mathematics · Medium
→If A and B partially overlap, how are A − B, A ∩ B, and B − A represented in the Venn diagram?
Class 10 · Mathematics · Easy
→If A ⊆ B, what are A ∪ B and A ∩ B, respectively?
Class 10 · Mathematics · Medium
→If n(A ∪ B) = n(A) + n(B), what is the correct conclusion about A and B in a Venn diagram?
Class 10 · Mathematics · Medium
→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?
Class 10 · Mathematics · Medium
→In a group, 35% of people are in A, 48% are in B, and 20% are in both. What percentage is in at least one of the two sets?
Class 10 · Mathematics · Medium
→In a school of 120 students, 68 chose A, 57 chose B, and 31 chose both. What percentage chose at least one of A or B?
Class 10 · Mathematics · Hard
→If n(A) = 4x + 6, n(B) = 3x + 9, n(A ∩ B) = 2x + 5, and n(A ∪ B) = 80, find x.
Class 10 · Mathematics · Hard
→If n(A) = 3x + 8, n(B) = 2x + 17, n(A ∩ B) = x + 5, and n(A ∪ B) = 60, what is x?
Class 10 · Mathematics · Medium
→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?
Class 10 · Mathematics · Hard
→If n(A − B) = x + 5, n(B − A) = 2x − 3, n(A ∩ B) = x + 1, and n(A ∪ B) = 43, what is the value of x?
Class 10 · Mathematics · Medium
→In a Venn diagram, the shaded region is outside both A and B. Which representation is correct?
Class 10 · Mathematics · Easy
→In a Venn diagram, the shaded region is inside A and outside B. How is it represented?
Class 10 · Mathematics · Medium
→If A ∩ B = ∅ and B ∩ C = ∅, is it necessary that A ∩ C = ∅?
Class 10 · Mathematics · Easy
→If in the Venn diagram of A and B, the circle of A lies completely inside the circle of B, which statement is necessarily true?
Class 10 · Mathematics · Hard
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