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Class 10 · Mathematics · Medium
→If n(A − B) = 3x + 2, n(B − A) = 2x + 5, n(A ∩ B) = x + 4, and n(A ∪ B) = 71, what is x?
Class 10 · Mathematics · Medium
→If n(A) = 5x + 4, n(B) = 4x + 7, n(A ∩ B) = 2x + 3, and n(A ∪ B) = 78, what is the value of x?
Class 10 · Mathematics · Medium
→If n(A ∪ B ∪ C) = 135, exactly one set contains 58 elements, and exactly two sets contain 49 elements, what is n(A ∩ B ∩ C)?
Class 10 · Mathematics · Hard
→In three clubs, n(A) = 72, n(B) = 68, n(C) = 61, n(A ∩ B) = 29, n(B ∩ C) = 24, n(C ∩ A) = 26, and n(A ∩ B ∩ C) = 11. How many members are only in B?
Class 10 · Mathematics · Medium
→If A ∩ B = ∅, n(A) = 44, n(B) = 52, and n(U) = 130, what is n((A ∪ B)′)?
Class 10 · Mathematics · Easy
→If A ⊆ B, n(B) = 83, n(A) = 47, and n(U) = 120, what is n(B − A)?
Class 10 · Mathematics · Medium
→If n(A) = 64, n(B) = 59, and n(A ∪ B) = 91, what is n(A △ B)?
Class 10 · Mathematics · Medium
→In a class of 95 students, 56 study Mathematics, 49 study Science, and 27 study both subjects. How many students study exactly one subject?
Class 10 · Mathematics · Medium
→If n(A∩B′)=29, n(A′∩B)=33, n(A∩B)=17, and n((A∪B)′)=21, what is n(U)?
Class 10 · Mathematics · Medium
→If n(U)=140, n(A′)=58, n(B′)=71, and n(A∩B)=34, what is n(A∪B)?
Class 10 · Mathematics · Easy
→If n(A∪B)=112, n(A−B)=43, and n(B−A)=37, what is n(A∩B)?
Class 10 · Mathematics · Easy
→In a Venn diagram, only A has 18 elements, only B has 22, only C has 16, only A∩B has 11, only B∩C has 13, only C∩A has 9, and all three have 6 elements. How many elements are in at least two sets?
Class 10 · Mathematics · Medium
→If n(A)=78, n(B)=69, n(C)=63, n(A∩B)=30, n(B∩C)=25, n(C∩A)=21, and n(A∩B∩C)=9, how many elements are only in set A?
Class 10 · Mathematics · Medium
→In a survey, n(U)=210, n(A)=96, n(B)=88, n(C)=74, n(A∩B)=39, n(B∩C)=31, n(C∩A)=28, and n(A∩B∩C)=14. How many people are in none of the sets?
Class 10 · Mathematics · Medium
→Let U={1,2,...,60}, A be the set of multiples of 3, and B be the set of multiples of 4. What is n((A∪B)′)?
Class 10 · Mathematics · Medium
→If n(A)=4x+5, n(B)=3x+8, n(A∩B)=2x+1, and n(A∪B)=72, what is the value of x?
Class 10 · Mathematics · Easy
→If only A has 21 elements, only B has 24, only C has 18, only A∩B has 13, only B∩C has 11, only C∩A has 9, and all three sets have 7 elements, how many elements belong to exactly two sets?
Class 10 · Mathematics · Medium
→In a survey, n(U)=180, n(A)=82, n(B)=76, n(C)=69, n(A∩B)=34, n(B∩C)=29, n(C∩A)=27, and n(A∩B∩C)=12. How many people are in none of the sets?
Class 10 · Mathematics · Hard
→If n(A ∪ B ∪ C) = 140, exactly one set has 65 elements and exactly two sets have 51 elements, what is n(A ∩ B ∩ C)?
Class 10 · Mathematics · Medium
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