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} and B = {b, d}, find B′.If U = {2, 4, 6, 8, 10} and A = {4, 8}, which one is A′?If U = {x : x ∈ N, x ≤ 6} and A = {1, 2, 3}, what is A′?If U = {x ∈ ℤ : −2 ≤ x ≤ 2} and A = {−1, 0, 1}, find A′, the complement of A with respect to U.If U = {p, q, r} and A = ∅, what is A′, the complement of A with respect to U?With respect to the universal set \(U\), for a set \(A\), what is \((A')'\) equal to?If \(U=\{1,2,3,4,5,6,7\}\) and \(A'=\{2,4,6\}\), what is \(A\)?If \(U=\{a,e,i,o,u\}\) and \(V'=\{e,o\}\), what is \(V\)?If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{x:x\in U,\ x\text{ is even}\}\), which set is \(A'\)?If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{x:x\in U,\ x<5\}\), what is \(A'\)?If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{x:x\in U,\ x\ge 7\}\), what is \(A'\)?If \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\) and \(A=\{3,6,9,12\}\), how many elements does \(A'\) contain?If \(n(U)=30\) and \(n(A)=18\), what is the value of \(n(A')\)?If \(n(U)=50\) and \(n(A')=22\), find \(n(A)\).If, for a universal set \(U\), \(n(A)=15\) and \(n(A')=35\), what is \(n(U)\)?If the universal set U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, and B = {3, 4, 5}, what is (A ∪ B)′?If the universal set is U = {a, b, c, d, e}, A = {a, b, d}, and B = {b, c, d}, what is the complement of A ∩ B with respect to U?If U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3, 4}, and B = {3, 4, 5}, what is A′ ∩ B′?If U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 3, 5}, and B = {2, 3, 6}, what is A′ ∪ B′?If A ⊆ U, which is the most correct definition of A′?