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 = (−∞, 2], what is A′?If U = {1,2,3,4,5,6,7,8}, A′ = {1,4,7}, and B′ = {2,4,8}, what is A ∩ B?If U = {1,2,3,4,5,6,7,8,9,10,11,12} and A = {2,3,5,7,11}, what is the correct description of A′?If U = {a, b, c, d, e, f, g, h}, A = {a, b, c, d}, and B = {c, d, e, f}, how many elements are in A' Δ B'?If U = {1, 2, ..., 12} and A = {x : x is a divisor of 12}, what is A'?If U = N and A = {x : x is an even natural number}, what does A′ represent?Let U = {x : x is a positive integer less than 10} and A = {x : x² < 20}. What is A′?If U={1,2,3,4,5,6} and A'={2,4,6}, what is A?If \(U=\{1,2,\ldots,10\}\) and \(A=\{x\in U:x\text{ is a multiple of 2 or 3}\}\), what is \(A'\)?If U = {1, 2, ..., 9}, A = {1, 2, 3, 4}, and B = {3, 4, 5, 6}, what is the complement of A ∩ B with respect to U?Let U = {x : x ∈ Z, −3 ≤ x ≤ 3} and A = {x : x ≥ 0}. What is the complement A' with respect to U?If U = {1, 2, ..., 18} and A = {x : x is a prime factor of 18}, what is n(P(A'))?If \(n(U)=30\) and \(n(A)=11\), what is \(n(A')\)?In a Venn diagram, what is A' ∪ B' equal to?If n(U) = 50, n(A) = 20, n(B) = 16, and n(A ∩ B) = 6, how many elements are in neither A nor B?If n(U) = 32 and n(A ∩ B) = 9, how many elements are in (A ∩ B)'?If the universal set U = {1, 2, 3, 4, 5} and A = {2, 5}, what is the complement A′?If \(n(U)=38\) and \(n(A)=16\), what is \(n(A')\)?If U = {1, 2, 3, 4, 5, 6} and A = {1, 4, 6}, what is A', the complement of A in U?If U = {a, b, c, d, e, f}, A = {a, b, d}, and B = {b, c, d}, what is (A ∪ B)'?