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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 U = {1,2,...,20}, A is the set of even numbers in U, and B is the set of multiples of 5 in U, which set does Aᶜ ∩ Bᶜ represent?If |U| = 80, |A| = 35, |B| = 40, and |A ∩ B| = 15, what is |(A ∪ B)ᶜ|?If |U| = 100, |A'| = 58, |B'| = 47, and |A ∩ B| = 21, what is the value of |(A ∪ B)'|?If A − B = A ∩ B', then (A − B)' is equal to which expression?If U = ℝ and A = (2, 7], what is A′?If U = R, A = (−∞, 3), and B = [1, ∞), what is (A ∩ B)'?If A' ∩ B' = ∅, what is the correct conclusion about A ∪ B?If (A ∩ B)′ = A′ ∩ B′ holds in a universal set U, what can be said about A and B?If U = {1, 2, ..., 50}, A is the set of multiples of 2, and B is the set of multiples of 5, what is |A' ∩ B'|?If U = {a, b, c, d, e, f, g, h}, A' = {b, d, f, h}, and B = {a, b, c, d}, what is A ∩ B'?If A ∪ A′ = U and A ∩ A′ = ∅, what kind of set is A′ with respect to A?If U = {x : x ∈ ℕ, x ≤ 40}, A is the set of numbers divisible by 4, and B is the set of numbers divisible by 6, what is |(A ∩ B)′|?If \(U=\mathbb{R}\) and \(A=\{x:x^2-5x+6=0\}\), which is the correct description of \(A'\)?If U = {1, 2, ..., 12}, A = {1, 3, 5, 7, 9, 11}, and B = {2, 3, 5, 7, 11}, what is (A′ ∪ B′)′?If \(A'=B'\), what is the correct conclusion for \(A\) and \(B\)?If \(U=\{1,2,\ldots,60\}\), \(A\) is the set of multiples of 3, \(B\) the set of multiples of 4, and \(C\) the set of multiples of 5, what is \(|(A\cup B\cup C)'|\)?In a universal set \(U\) of 120 students, 70 study mathematics, 65 study physics, and 30 study both. How many study neither mathematics nor physics?If \(U=\{x:x\in\mathbb{Z},0\le x\le15\}\) and \(A=\{x:x\text{ is prime}\}\), which element must be in \(A'\)?If \(U=\{1,2,\ldots,10\}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5,6\}\), what is \(A'\Delta B'\) equal to?If the universal set is \(U=\mathbb{R}\) and \(A=\{x\in\mathbb{R}:x<2\text{ or }x\ge8\}\), what is \(A'\)?