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 = R and A = {x | x ≤ 1 or x > 9}, what is A'?For subsets A and B of a universal set U, which statement correctly represents De Morgan’s law?If U = {1, 2, ..., 30}, A is the set of numbers divisible by 2, and B is the set of numbers divisible by 3, what is |A' ∪ B'|?If U = ℝ and A = [0, 4) ∪ (7, 10], what is A′?Which statement is always false if U ≠ ∅?If U = {1, 2, …, 50}, A = {x : x is divisible by 4}, and B = {x : x is divisible by 6}, what is |A′ ∩ B|?If U = {1,2,…,18} and A′ = {2,3,5,7,11,13,17}, how many elements are in A?If U = R and A = {x ∈ R : x² − 9 > 0}, what is A′?If U = {1, 2, …, 12}, A = {1, 2, 3, 4, 5, 6}, and B = {4, 5, 6, 7, 8}, what is (A − B)′?If U = {1,2,…,100} and A = {x : x is not divisible by 7}, what is |A′|?If A △ B = (A ∩ B′) ∪ (A′ ∩ B), what is (A △ B)′ equal to?If U = {1,2,…,20}, A = {x : x is even}, and B = {x : x is prime}, how many elements are in A′ ∩ B′?If U = R and A = (−∞,−4] ∪ (3,∞), what is A′?If \(A \cup B' = B'\), which of the following conclusions is always true?If \(U=\{1,2,\ldots,60\}\), \(A=\{x:x\text{ is divisible by }6\}\), and \(B=\{x:x\text{ is divisible by }10\}\), what is \(|(A\cap B)'|\)?If \(U=\{1,2,\ldots,16\}\), \(A=\{1,4,9,16\}\), and \(B=\{2,4,6,8,10,12,14,16\}\), what is \(A\cap B'\)?If \(U=\{x:x\in\mathbb N, x\le 35\}\) and \(A=\{x:x\text{ is a composite number}\}\), what type of elements will be in \(A'\)?If \(U=\mathbb R\), \(A=\{x:-1\le x<5\}\), and \(B=\{x:2<x\le 8\}\), what is \(A'\cup B'\)?If the complement of \(A\) with respect to the universal set \(U\) is \(A'=\varnothing\), which statement about \(A\) is correct?If the universal set is \(U=\{1,2,\ldots,27\}\), \(A=\{x\in U:x\text{ is a multiple of }3\}\), and \(B=\{x\in U:x\text{ is a multiple of }9\}\), how many elements are in \(A'\cup B\)?