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 \(U=\{x:x\in\mathbb{Z},0\le x\le15\}\) 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 \(A'\)?If \(U=\mathbb{R}\) and \(A=\{x:x^2<16\}\), what is \(A'\)?If \(A\cap B=A\cap C\) and \(A'\cap B=A'\cap C\), what is the correct conclusion about \(B\) and \(C\)?If U = {1, 2, ..., 25}, A = {x : x is odd} and B = {x : x is a perfect square}, what is |A' ∩ B|?If U = {x : x ∈ N, x ≤ 100} and A = {x : x is not divisible by 2}, then A' is the set of what?If (A ∪ B)' = ∅ and A ∩ B = ∅, then B is equal to what?If U = {1, 2, ..., 18} and A = {2, 4, 6, 8, 10, 12, 14, 16, 18}, what is (A')'?If U = {1, 2, ..., 20} and A = {x : x is divisible by 3}, how many elements are in A'?If U = {x : x ∈ Z, -3 ≤ x ≤ 6} and A = {x : x ≥ 2}, what is A'?If U = {1, 2, ..., 30} and A = {x : x is divisible by 2 or 3}, how many elements are in A'?If U = {1, 2, ..., 16}, A = {1, 2, 4, 8, 16}, and B = {2, 4, 6, 8, 10, 12, 14, 16}, then B - A is equal to:If U = R, A = [-2, 5) and B = (0, 7], what is (A ∪ B)'?If U = R, A = (-3, 4], and B = [1, 6), what is A' ∩ B'?If the universal set is U = {1, 2, ..., 100} and A = {x ∈ U : x is a perfect square}, what is the value of |A′|?If U = {1, 2, ..., 15}, A = {1, 4, 9}, and B = {2, 4, 6, 8, 10, 12, 14}, how many elements are in (A ∩ B)′?If U has n elements and A has r elements, how many elements are in A′?If A ⊆ U, what are A ∪ A′ and A ∩ A′, respectively?If A ⊆ B in a universal set U, which of the following relations is always true?