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Subjects

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

Which pair of properties is most useful for checking whether a set claimed to be A^c is actually the complement of A?If \(U=\{2,3,4,5,6\}\) and \(A=\{3,6\}\), what is \(A^c\)?If \(U=\{p,q,r,s,t\}\) and \(A=\{p,s,t\}\), find \(A^c\).If \(x\in A^c\), which statement is definitely true?If \(U=\{5,10,15,20\}\) and \(A=U\), what is \(A^c\)?If \(U=\{7,8,9\}\) and \(A=\varnothing\), what is \(A^c\)?If \(n(U)=36\) and \(n(A)=14\), what is \(n(A^c)\)?If U = {1, 2, 3, 4, 5, 6, 7} and Aᶜ = {1, 7}, what is A?If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {1, 3, 5, 7}, what is Aᶜ?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 4, 9}, what is the complement Aᶜ of A with respect to U?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} and A = {4, 8, 12}, what is the complement Aᶜ with respect to U?If U = {0, 1, 2, 3, 4, 5, 6} and A = {0, 3, 6}, what is the complement Aᶜ of A with respect to U?If U = {x : x ∈ N, 1 ≤ x ≤ 10} and A = {x : x is even}, what is the complement Aᶜ with respect to U?Assume that N denotes the set of positive natural numbers. If U = {x ∈ N : x < 7} and A = {x ∈ U : x ≤ 3}, what is the complement Aᶜ of A with respect to U?If U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 5}, and B = {2, 4, 6}, what is the complement of A ∪ B?If the universal set U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, and B = {3, 4, 5}, what is (A ∩ B)ᶜ with respect to U?If A ⊆ B, which relation is always correct?With respect to a universal set \(U\), which of the following statements is always true for every set \(A\)?If \(U\) is the set of all students in a school and \(A\) is the set of students who come by bus, what does \(A^c\) represent?If \(U=\{\text{red},\text{blue},\text{green},\text{yellow}\}\) and \(A=\{\text{red},\text{yellow}\}\), what is \(A^c\)?