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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

If n(U) = 84 and n(A) = 2n(Aᶜ), where U is the universal set, what is n(Aᶜ)?For the universal set U, if n(U)=72 and n(A^c)=3n(A), what is the value of n(A)?If Aᶜ = {x | x ∈ U and x ∉ A}, why does A ∪ Aᶜ = U hold?If U = {1,2,3,4,5,6,7,8,9} and A = {2,3,5}, which of the following sets B is not the complement of A?If U = {1,2,3,...,80} and A is the subset of U whose elements are divisible by 8, how many elements does Aᶜ contain?Let the universal set be \(U=\{1,2,3,\ldots,12\}\), \(A=\{2,3,5,7,11\}\), and \(B=A^c\). What is the value of \(A\cup B\)?If the universal set is \(U=\{1,2,3,\ldots,12\}\), \(A=\{3,6,9,12\}\), and \(B=A^c\), what is the value of \(A\cap B\)?If the universal set is \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4,5\}\), and \(B=\{6,7,8\}\), what is the value of \((A\cup B)^c\)?If the universal set is \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,4,6\}\), what is the value of \((A\cap B)^c\)?If the universal set is \(U=\{1,2,3,4,5,6\}\) and \(A=\{2,4,6\}\), what is \(A^c\)?If the universal set is \(U=\{a,b,c,d,e\}\) and \(B=\{a,e\}\), how many elements does \(B^c\) contain?If \(A=\varnothing\) and the universal set is \(U\), what is \(A^c\)?If \(A=U\), what is \(A^c\)?Given the universal set \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,3,5,8\}\), what is the value of \((A\cup B)^c\)?If \(A\subseteq B\), which relation between their complements is correct?If n(U) = 40 and n(A) = 18, what is n(Aᶜ)?In a class of 60 students, 35 students play cricket. How many students do not play cricket?If U = {x ∈ ℕ : x ≤ 10} and A = {x ∈ U : x is even}, what is Aᶜ?If U = ℤ and A = {x ∈ ℤ : x > 0}, what does Aᶜ represent?If U = ℝ and A = (2, 5), what is Aᶜ?