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, ..., 100}, A = {x ∈ U : 10 divides x}, and B = {x ∈ U : 15 divides x}, what is n(A′ ∪ B′)?If U = R, A = [−7, −1), and B = (−3, 5], what is (A ∩ B)′?If U = {1, 2, ..., 24}, A is the set of odd numbers in U, and B is the set of prime numbers in U, what is A ∩ B′?If A ⊆ U, what is (A′ ∩ A)′ equal to?If U = {1, 2, ..., 50} and A = {x : x ∈ U, the last digit of x is 2 or 7}, what is n(A′)?If U = {x : x ∈ Z, −9 ≤ x ≤ 9} and A = {x : x ∈ U, |x| > 4}, what is A′?If the universal set is \(U=\mathbb{R}\), \(A=\{x\in\mathbb{R}:x\ne 0\}\), and \(B=\{x\in\mathbb{R}:x\ne 1\}\), what is \(A'\cup B'\)?If \(U=\{1,2,\ldots,35\}\), \(A=\{x\in U:5\mid x\}\), and \(B=\{x\in U:x\text{ is odd}\}\), what is \(B'\cap A\)?If the universal set \(U=\{1,2,\ldots,16\}\), \(A=\{1,2,4,8,16\}\), and \(B=\{3,6,9,12,15\}\), what is the complement of \(A\cup B\) relative to \(U\)?If the universal set is \(U=\mathbb{R}\), \(A=(-\infty,2]\), and \(B=[-1,\infty)\), what is \(A'\cap B'\)?If \(U=\{1,2,\ldots,27\}\), \(A=\{x\in U:3\mid x\}\), and \(B=\{x\in U:9\mid x\}\), what is \(A\cap B'\)?If U = {1, 2, ..., 49} and A = {x : x ∈ U, x is a perfect square}, how many numbers divisible by 7 are in A′?If the universal set is \(U=\mathbb{R}\) and \(A=\{x\in\mathbb{R}\mid x<3\text{ or }x\ge 8\}\), what is \(A'\)?If \(U=\{1,2,\ldots,60\}\), \(A=\{x:x\in U,2\mid x\}\), and \(B=\{x:x\in U,3\mid x\}\), what is \(n(A'\cap B')\)?If \(U=\{x\in\mathbb{Z}:-3\le x\le 8\}\), \(A=\{x\in U:x+1\ge4\}\), and \(B=\{x\in U:x<6\}\), what is \(A'\cup B'\)?If U = {1, 2, ..., 32} and A = {x : x ∈ U, x is even}, how many ordered pairs are in A' × A'?With respect to the universal set U, which of the following De Morgan identities is true for every pair of sets A and B?If U = {1, 2, ..., 25} and A' = {4, 8, 12, 16, 20, 24}, how many elements of A are divisible by 4?For subsets A and B of a universal set U, if A' = B', which conclusion is necessarily true?If U = {1, 2, ..., 54}, A = {x : x ∈ U and 6 divides x}, and B = {x : x ∈ U and 9 divides x}, what is n(A′ ∩ B)?