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
Let \(U_1=\{1,2,3,4\}\), \(U_2=\{1,2,3,4,5,6\}\), and \(A=\{1,2\}\). What is the set difference between the complement of \(A\) relative to \(U_2\) and the complement of \(A\) relative to \(U_1\), taking the former difference from the latter?If the universal set is \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5,6\}\), what is the value of \((A^c\cap B)^c\)?In the universal set U={1,2,3,4,5,6,7,8,9}, let A={2,4,6,8} and B={1,2,3,4}. If all complements are taken with respect to U, what is (Aᶜ∪B)ᶜ?Let U={x∈N: 1≤x≤18}, A={x: x is divisible by 3}, and B={x: x is even}. How many elements are in Aᶜ∩Bᶜ?If U={1,2,3,4,5,6,7,8,9,10,11,12}, A={1,2,3,4,5,6}, and B={2,4,6,8,10,12}, how many elements does Aᶜ∪Bᶜ contain?In the universal set U={1,2,3,4,5,6,7,8}, let A={1,2,3} and B={4,5}. Find Aᶜ∩Bᶜ.If U={1,2,3,4,5,6,7,8,9,10} and Aᶜ={1,4,9}, how many elements does A contain?For a finite universal set U, n(U)=64 and n(A)=3n(Aᶜ). What is the value of n(Aᶜ)?If U has n(U)=54 and a set A satisfies n(Aᶜ)=2n(A), what is the value of n(A)?If A⊆U and Aᶜ={x∈U: x∉A}, why is A∩Aᶜ empty?If U={1,2,3,4,5,6,7,8} and A={1,2,3}, which of the following is not the complement of A?Which of the following is the correct De Morgan’s law for complements of two sets with respect to the universal set?If the universal set is \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,3,5,7,9\}\), and \(B=A^c\), what is the value of \(A\cup B\)?If the universal set is \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,4,6,8,10\}\), and \(B=A^c\), what is the value of \(A\cap B\)?If the universal set is \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\), and \(B=\{5,6,7,8\}\), what is \((A\cup B)^c\)?With respect to a universal set, which relation holds between a set and its complement?If \(U=\{1,2,3,\ldots,18\}\), \(A=\{x:x\text{ is divisible by }2\}\), and \(B=\{x:x\text{ is divisible by }3\}\), how many elements are in \(A^c\cap B^c\)?If \(U=\{1,2,3,\ldots,16\}\), \(A=\{1,4,9,16\}\), and \(B=\{2,4,6,8,10,12,14,16\}\), what is \((A\cup B)^c\)?If \(U=\{1,2,3,\ldots,20\}\), \(A=\{x:x\text{ is prime}\}\), and \(B=\{x:x\text{ is odd}\}\), what is \(A^c\cap B\)?If the universal set \(U=\{x\in\mathbb Z\mid -5\le x\le 5\}\) and \(A=\{x\in\mathbb Z\mid x^2<9\}\), what is the complement \(A^c\) of A?