Mathematics
Venn Diagrams
Practice questions
In a Venn diagram, n(A ∪ B)=63 and n(A ∩ B)=17. How many elements are in exactly one set?Sets A and B are disjoint. Which statement is correct?What region does \((A\cap B)^c\) represent in a Venn diagram?According to De Morgan's law, what is \((A\cup B)^c\) equal to?According to De Morgan's law, what is \((A\cap B)^c\) equal to?If \(n(U)=75\) and \(n(A\cap B)=18\), what is \(n((A\cap B)^c)\)?In an exam, 36 students chose Hindi, 42 chose English, and 20 chose both subjects. How many students chose exactly one subject?Among 65 people, 31 like cricket, 29 like football, and 11 like both. How many like neither sport?If \(n(A\cup B)=72\), \(n(A)=46\), and \(n(B-A)=26\), what is \(n(A\cap B)\)?In a Venn diagram, \(n(A-B)=18\), \(n(A\cap B)=12\), \(n(B-A)=22\), and 8 elements are outside. What is \(n(U)\)?If \(n(U)=55\), \(n(A-B)=14\), \(n(A\cap B)=9\), and \(n(B-A)=17\), what is the number of elements outside \(A\cup B\)?In a three-set Venn diagram, \(n(A\cap B)=12\), \(n(B\cap C)=13\), \(n(C\cap A)=10\), and \(n(A\cap B\cap C)=4\). How many elements lie in exactly two of the sets?If n(A)=25, n(B)=22, n(C)=19, n(A∩B)=7, n(B∩C)=6, n(C∩A)=5, n(A∩B∩C)=2, and n(U)=60, how many elements are in none of the sets?If only A=11, only B=13, only C=9, only (A∩B)=5, only (B∩C)=4, only (C∩A)=6, and A∩B∩C=3, what is n(A∪B∪C)?In a Venn diagram, the shaded region represents A ∩ Bᶜ. Which set is equal to this region?In a survey, n(U) = 95, n(A) = 48, n(B) = 39, and n((A ∪ B)ᶜ) = 20. According to the Venn diagram, what is n(A ∩ B)?In a Venn diagram, n(U)=90, n(A)=46, n(B)=38, and n(A∩B)=16. What is n(A∪B)?If n(A)=52, n(B)=47, and n(A∪B)=79, what is n(A∩B)?In a survey, n(U)=120, n(A)=61, n(B)=54, and n(A∩B)=25. How many elements are in neither set?If n(A)=44 and n(A∩B)=19, how many elements are only in set A in a Venn diagram?