Mathematics
Venn Diagrams
Practice questions
In a Venn diagram, the shaded region is outside both A and B. Which representation is correct?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?If n(A) = 3x + 8, n(B) = 2x + 17, n(A ∩ B) = x + 5, and n(A ∪ B) = 60, what is x?If n(A) = 4x + 6, n(B) = 3x + 9, n(A ∩ B) = 2x + 5, and n(A ∪ B) = 80, find x.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?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?If n(A ∪ B) = n(A) + n(B), what is the correct conclusion about A and B in a Venn diagram?If A ⊆ B, what are A ∪ B and A ∩ B, respectively?If A and B partially overlap, how are A − B, A ∩ B, and B − A represented in the Venn diagram?If n(A ∩ B′) = 29, n(A′ ∩ B) = 34, and n(A ∩ B) = 21, what is n(A ∪ B)?If n(A ∩ B′) = 18, n(A′ ∩ B) = 22, n(A ∩ B) = 16, and n(U) = 75, what is n(A′ ∩ B′)?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)?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)?If n(A − B) = 27, n(B − C) = 31, n(C − A) = 24, and the three sets are drawn generally, why is n(A ∪ B ∪ C) not determined from these alone?Why do A, B, and C create 7 separate inner regions in a Venn diagram?If n(U) = 250, n(A) = 120, n(B) = 110, n(C) = 95, n(A ∩ B) = 52, n(B ∩ C) = 41, n(C ∩ A) = 37, and n(A ∩ B ∩ C) = 19, what is the number of elements not in at least one set?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)')?