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Class 10 · Mathematics · Medium
→If n(A ∪ B) = 126, n(A − B) = 48, and n(B − A) = 41, then what is n(A ∩ B)?
Class 12 · Mathematics · Medium
→If n(A ∪ B ∪ C) = 162, exactly one set contains 73 elements and exactly two sets contain 56 elements, then what is n(A ∩ B ∩ C)?
Class 10 · Mathematics · Medium
→In a Venn diagram, only A has 26 elements, only B has 31, only C has 24, only A ∩ B has 14, only B ∩ C has 16, only C ∩ A has 12, and all three have 9 elements. How many elements are in exactly one set?
Class 10 · Mathematics · Hard
→If n(A) = 86, n(B) = 79, n(C) = 71, n(A ∩ B) = 34, n(B ∩ C) = 29, n(C ∩ A) = 27, and n(A ∩ B ∩ C) = 12, then how many elements are only in C?
Class 10 · Mathematics · Hard
→In a survey, n(U) = 240, n(A) = 112, n(B) = 104, n(C) = 93, n(A ∩ B) = 46, n(B ∩ C) = 38, n(C ∩ A) = 35, and n(A ∩ B ∩ C) = 17. How many elements are in none of the sets?
Class 10 · Mathematics · Hard
→If n(A ∪ B ∪ C) = 155, n(A ∪ B) = 118, n(B ∪ C) = 124, n(C ∪ A) = 121, and n(B) = 64, then what is n((A ∩ C) − B)?
Class 10 · Mathematics · Easy
→In a Venn diagram, n(A ∪ B ∪ C) = 190 and n((A ∪ B ∪ C)′) = 25. What is n(U)?
Class 10 · Mathematics · Medium
→Assertion: If A ∩ B = ∅, then n(A ∪ B) = n(A) + n(B). Reason: Disjoint sets have no common elements or common region. Choose the correct option.
Class 10 · Mathematics · Medium
→Assertion: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Reason: Elements of A ∩ B are counted twice in n(A) + n(B). Choose the correct option.
Class 10 · Mathematics · Hard
→If only n(A−B)=20, n(B−C)=18, and n(C−A)=16 are given, can n(A ∪ B ∪ C) be determined uniquely?
Class 10 · Mathematics · Medium
→If n(A ∪ B ∪ C) = 160, n(A) = 70, n(B) = 75, n(C) = 80 and n(A ∩ B ∩ C) = 18, then what is n(A ∩ B) + n(B ∩ C) + n(C ∩ A)?
Class 10 · Mathematics · Easy
→If n(A − B)=0 and n(A)>0, which relation between A and B is necessarily true in the Venn diagram?
Class 10 · Mathematics · Easy
→If A ⊆ B ⊆ C, then what is A ∩ B ∩ C equal to?
Class 10 · Mathematics · Easy
→If A ⊆ B ⊆ C, then what is A ∪ B ∪ C equal to?
Class 10 · Mathematics · Medium
→If A, B and C are mutually disjoint, n(A) = 18, n(B) = 24, n(C) = 29 and n(U) = 90, then what is n((A ∪ B ∪ C)')?
Class 10 · Mathematics · Easy
→Which statement correctly describes the Venn region represented by A ∩ (B − C)?
Class 10 · Mathematics · Medium
→If n(A ∩ (B ∪ C)) = 44, only (A ∩ B) contains 18 elements and only (A ∩ C) contains 16 elements, then what is n(A ∩ B ∩ C)?
Class 10 · Mathematics · Hard
→Suppose n(A)=70, n(B)=65, n(C)=60, n(A ∪ B ∪ C)=128, n(A ∩ B)=27, n(B ∩ C)=24, and n(C ∩ A)=22. Which conclusion is mathematically correct?
Class 10 · Mathematics · Medium
→If only A has 31 elements, only B has 27 elements, only C has 25 elements, the total of the exactly-two-set regions is 42, and all three sets have 11 elements, then what is n(A ∪ B ∪ C)?
Class 10 · Mathematics · Hard
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