Mathematics
Venn Diagrams
Practice questions
If n(A△B)=78 and n(A−B)=34, what is n(B−A)?Among 90 students, 43 like Chemistry, 39 like Biology, and 18 like both subjects. How many like neither subject?If n(A) = 49, n(B) = 52, and A ∩ B = ∅, how many elements belong to exactly one of the two sets?If n(A ∪ B) = 88, n(A − B) = 31, and n(B − A) = 29, what is n(A ∩ B)?In three sets, n(A ∩ B ∩ C) = 14. Which region of the Venn diagram does this represent?If only A = 18, only B = 22, only C = 19, only A ∩ B = 9, only B ∩ C = 8, only C ∩ A = 7, and A ∩ B ∩ C = 6, what is n(A ∪ B ∪ C)?In three sets, only A = 27, only A ∩ B = 10, only C ∩ A = 12, and A ∩ B ∩ C = 8. What is n(A)?In a three-set Venn diagram, only B = 24, only A ∩ B = 11, only B ∩ C = 13, and A ∩ B ∩ C = 9. What is n(B)?Given n(U) = 180, n(A) = 76, n(B) = 69, n(C) = 62, n(A ∩ B) = 30, n(B ∩ C) = 27, n(C ∩ A) = 24, and n(A ∩ B ∩ C) = 10, how many elements belong to none of the sets?If n(A) = 48, n(B) = 43, n(C) = 41, n(A ∪ B ∪ C) = 99, n(A ∩ B) = 17, n(B ∩ C) = 14, and n(C ∩ A) = 13, what is n(A ∩ B ∩ C)?If n(A ∪ B) = 73, n(A − B) = 28, and n(B − A) = 32, which statement is correct?In a survey, n(U) = 150, n(A) = 70, n(B) = 62, and n((A ∪ B)ᶜ) = 32. What is n(A ∩ B)?If n(A ∪ B) = 96, n(A) = 58, and n(A − B) = 29, what is n(B − A)?If n(A) = 46, n(B) = 40, n(C) = 37, n(A ∩ B) = 14, n(B ∩ C) = 12, n(C ∩ A) = 11, and n(A ∪ B ∪ C) = 91, what is n(A ∩ B ∩ C)?In a Venn diagram, which set represents all elements that belong to A but not to B?If A ⊆ B ⊆ C, n(C) = 95, n(B) = 61, and n(A) = 28, what is n(C − B)?In a sports survey, 80 people like cricket, 64 like football, and 29 like both. How many like exactly one sport?In a Venn diagram, n(U) = 180, n(A) = 92, n(B) = 84, and n((A ∪ B)ᶜ) = 38. What is n(A ∩ B)?In a class, n(A) = 74, n(B) = 68, and 86 students are in exactly one set. What is n(A ∩ B)?If n(U) = 120, n(A) = 77, and n(B) = 64, what is the minimum possible value of n(A ∩ B)?