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 the universal set is U = {1, 2, …, 12} and A′ = {1, 5, 7, 11}, what is the set A?If the universal set is U = ℝ and A = {x : x ≤ −1 or x > 4}, what is A′?If U has 200 students, 120 take Hindi, 90 take English, and 50 take both languages, how many take neither language?If A ∩ B′ = ∅, which conclusion is always true?If A ∪ B′ = U, which relation is always true?If the universal set is \(U=\{1,2,\ldots,36\}\), \(A\) is the set of multiples of 4, and \(B\) is the set of multiples of 9, what is the value of \(|A'\cap B'|\)?If the universal set is \(U=\mathbb{R}\) and \(A=\{x:x^2-1\ge 0\}\), what is \(A'\)?If \(U=\{1,2,\ldots,45\}\), \(A\) is the set of numbers divisible by 3, and \(B\) is the set of numbers divisible by 5, what is \(|(A\cap B)'|\)?If \(U=\mathbb{R}\) and \(A=\{x:-2<x\le6\}\), what is \(A'\)?If \(U=\{1,2,\ldots,72\}\), \(A\) is the set of multiples of 4, and \(B\) is the set of multiples of 9, what is \(|(A\cup B)'|\)?If \(U=\{x:x\in\mathbb{Z},-8\le x\le8\}\) and \(A=\{x:x^2-4x\le0\}\), what is \(A'\)?If \(A\subseteq B'\), which of the following relations is always true?If \(U=\{1,2,\ldots,40\}\), \(A\) is the set of prime numbers, and \(B\) is the set of odd numbers, what is \(|A'\cap B|\)?What is ((A' ∩ B)') equal to?If U = R and A = {x : |x − 3| < 5}, what is A'?If \(A\cup B=U\), what is the value of \(A'\cap B'\)?If U = {1, 2, ..., 90}, and A, B, C are respectively the sets of multiples of 2, 3, and 5, what is |(A ∪ B ∪ C)'|?If U = {a, b, c, d, e, f, g, i, j, k}, A' = {b, e, i}, and B' = {a, d, j}, what is (A ∪ B)'?If U = {1, 2, ..., 25}, A is the set of perfect squares and B is the set of multiples of 5, which element belongs to A' ∩ B'?If A − B = ∅, which conclusion is always correct?