Mathematics
Complement of a Set and Its Properties
समुच्चय का पूरक और उसके गुणधर्म
In Class 11 Mathematics, under the chapter Sets, Complement of a Set and Its Properties explains the elements of a universal set that are not in a given set. Students find complements using notation such as A′, determine complements from given sets, and understand basic relationships between a set, its complement, and the universal set.
Practice questions
If n(U) = 64, only A has 18 elements, A ∩ B has 12 elements, and only B has 20 elements, how many elements are in the outside region, U − (A ∪ B)?In a Venn diagram, A∪A′ is equal to which set?In a Venn diagram, what is A∩A′ equal to?If n(U)=100, n(A)=45, n(B)=40, and n(A∩B)=15, what is n((A∪B)′)?If n(U) = 90 and n(A ∩ B) = 25, what is n((A ∩ B)′)?If \(n(U)=72\) and \(n(A)=29\), what is \(n(A')\)?If U={a,b,c,d,e,g}, A={a,c,e}, and B={b,c,g}, what is (A∪B)'?If n(U) = 110, n(A) = 58, n(B) = 47, and n(A ∩ B) = 20, what is n((A ∪ B)′)?If n(U) = 96 and n(A ∩ B) = 34, what is n((A ∩ B)′)?If n(U) = 92 and n(A ∪ B) = 67, how many elements are in the region that is neither in A nor in B in the Venn diagram?If U = {a, b, c, d, e, f, h}, A = {a, c, e}, and B = {c, d, f}, what is (A ∪ B)′?In a Venn diagram, n(U) = 100, n(A) = 52, n(B) = 44, and n(A ∩ B) = 21. What is n((A ∪ B)ᶜ)?If n(U) = 70, n(A) = 38, and n(Aᶜ) = 32, which statement is correct?Given \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{1,3,5,7\}\), what is the complement \(A^c\)?If \(n(U)=120\), \(n(A)=65\), \(n(B)=58\), and \(n(A\cap B)=29\), what is \(n(A^c\cap B^c)\)?If n(U) = 105 and n(A ∩ B) = 37, what is n((A ∩ B)ᶜ)?If U = {p, q, r, s, t, u, v} and A = {p, r, t, v}, what is Aᶜ, the complement of A with respect to U?If n(U)=110 and n(A∪B∪C)=92, how many elements belong to none of the sets?If n(Aᶜ) = 48 and n(U) = 95, what is n(A)?If n(U)=130 and n(A∩B)=46, what is n((A∩B)ᶜ)?