Mathematics
Venn Diagrams
Practice questions
In a class of 100 students, 72 chose at least one of A or B. If only A has 28 students and only B has 34 students, how many students are in both?In a survey, n(U) = 120, n(A) = 62, n(B) = 55, and n(A ∪ B) = 91. According to the Venn diagram, what is n(A ∩ B)?In a class, n(U) = 80, n(A) = 37, n(B) = 42, and n(A ∩ B) = 19. How many students belong only to A?If n(U) = 150, n(A) = 70, n(B) = 65, and n(A ∩ B) = 28, what is n((A ∪ B)')?If n(A ∩ B ∩ C) = 9, only A ∩ B has 14 elements, only B ∩ C has 11 elements, and only C ∩ A has 13 elements, what is n((A ∩ B) ∪ (B ∩ C) ∪ (C ∩ A))?In a survey, n(U) = 200 and n(A ∪ B ∪ C) = 164. How many people are in none of the sets?In a Venn diagram, only A has 23, only B has 17, only C has 19, the three two-set-only regions have 8, 9, and 10, and the centre has 5. What is n(A ∪ B ∪ C)?If A ∩ B = ∅, n(A) = 41, n(B) = 39, and n(U) = 100, what is n((A ∪ B)′)?In an examination group of 120 students, 72 study Mathematics, 64 study Physics, and 38 study both subjects. How many study exactly one subject?If n(U) = 110, n(A) = 58, n(B) = 49, and n(A − B) = 21, choose the correct value of n((A ∪ B)′).In a survey, n(M) = 60, n(P) = 54, n(C) = 50, n(M ∩ P) = 25, n(P ∩ C) = 22, n(C ∩ M) = 20, and n(M ∩ P ∩ C) = 10. How many study only M?Which Venn diagram region represents A − (B ∪ C)?If A and B are overlapping sets, which region is shaded for A ∪ B in a Venn diagram?If n(A ∩ B) = n(A) and n(A) > 0, what is the relation between A and B in a Venn diagram?If n(A) = 3x + 2, n(B) = 2x + 5, n(A ∩ B) = x + 1, and n(A ∪ B) = 30, what is the value of x?If n(A − B) = 2x + 3, n(B − A) = x + 7, n(A ∩ B) = x − 1, and n(A ∪ B) = 45, what is the value of x?In a Venn diagram, 14 elements lie outside both A and B, 22 lie only in A, 18 lie only in B, and 11 lie in both A and B. What is n(U)?If n(A ∪ B) = n(U), which region is empty in the Venn diagram?If A ∩ B = ∅ and B ∩ C = ∅, must A ∩ C = ∅?If A and B are disjoint, then what is (A ∪ B)' equal to?