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 \(U=\{a,b,c,d,e,f\}\) and \(A=\{a,c,f\}\), what is \(A'\)?If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{1,4,9\}\), how many elements does \(A'\) have?If \(A\) and \(B\) are subsets of \(U\), what is \((A\cap B)'\) equal to?If \(A\subseteq U\) and \(A'=\varnothing\), which conclusion is correct?If \(n(U)=80\) and \(n(A')=19\), what is \(n(A)\)?If U = {x ∈ N : 1 ≤ x ≤ 18} and A = {x ∈ U : 4 divides x}, how many elements are in the complement A′?If A = ∅ and the universal set U = {2, 4, 6}, what is A′?If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{2,4,6\}\), and \(B=\{4,6,8\}\), what is \(A'\cap B'\)?If U = {p,q,r,s,t}, A = {p,q,r}, and B = {r,s}, what is (A ∩ B)′?If A ⊆ B ⊆ U, which relation is correct for their complements?If U = {2, 4, 6, 8, 10, 12} and A' = {4, 10}, what is A?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7}, and B = {2, 3, 6, 7}, what is (A ∪ B)'?Let U = {x : x ∈ N, x ≤ 30} and let A be the set of positive divisors of 30 in U. What is n(A')?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {2, 4, 6, 8}, what is the complement A′ of A with respect to U?Let U = {x ∈ Z | −3 ≤ x ≤ 4} and A = {x ∈ U | x² < 4}. How many elements are in the complement A′ of A with respect to U?If U = {a,b,c,d,e}, A = {a,c,e}, and B = {b,c,d}, what is (A ∪ B)′?If |U| = 20, |A| = 12, |B| = 9, and |A ∩ B| = 5, what is |(A ∪ B)'|?If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {1, 3, 5, 7}, what is (A')'?If U = {x : x ∈ Z, 0 ≤ x ≤ 10} and A = {0, 2, 4, 6, 8, 10}, what is A'?If |U| = 15 and |A'| = 6, what is |A|?