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Subjects

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

Let A and B be two sets in a universal set U. Which of the following statements is always true?If U = {1, 2, ..., 20}, A = {x : x ∈ U and x ≤ 8}, and B = {x : x ∈ U and x ≥ 14}, what is (A ∪ B)′?If U = {x : x ∈ ℤ, −10 ≤ x ≤ 10} and A = {x : x ∈ U and |x| ≤ 3}, what is n(A')?If U = {1, 2, ..., 36} and A is the set of multiples of 6, how many multiples of 12 are in A′?If the universal set is U = ℝ, A = (−∞, 0] and B = [2, ∞), what is A′ ∩ B′?If U = {1, 2, ..., 10} and A = {x : x ∈ U and x² − 11x + 30 = 0}, what is A' ∩ {5, 6, 7, 8}?If U = {x : x ∈ ℕ, x ≤ 48}, A = {x ∈ U : 4 divides x}, and B = {x ∈ U : 6 divides x}, what is n((A ∪ B)′)?If U = {x : x ∈ Z, -8 ≤ x ≤ 8} and A = {x : x ∈ U, x² - 2x - 15 ≤ 0}, how many elements are in A′?If U = ℝ and A = (−∞, −2) ∪ [3, 7], what is A′, the complement of A in ℝ?If A ⊆ B ⊆ U, n(U) = 90, n(B) = 54, and n(A) = 31, what is n(A′ ∩ B)?If U = {1, 2, ..., 20}, A = {x : x ∈ U and x is even}, and B = {x : x ∈ U and x is prime}, what is A′ ∩ B?Let U = {1, 2, 3, …, 60}. If A = {x ∈ U : 4 divides x} and B = {x ∈ U : 9 divides x}, how many elements are in the complement of A ∪ B with respect to U?If U = {x : x ∈ Z, -10 ≤ x ≤ 10} and A = {x : x ∈ U, x² ≤ 16}, what is n(A′)?If U = ℝ and A = (−∞, −4] ∪ (2, 6), what is A′, the complement of A in ℝ?If A ⊆ B ⊆ U, n(U) = 150, n(A) = 64, and n(B) = 97, what is n(A′ ∩ B)?Let U = {1, 2, …, 30}, A = {x ∈ U : x is even}, and B = {x ∈ U : x is prime}. What is A′ ∩ B?If U = {a, b, c, d, e, f, g, h}, A = {a, d, g}, and B = {b, d, e, h}, what is A′ ∩ B′?If U = {1, 2, ..., 45}, A = {x ∈ U : 3 divides x}, and B = {x ∈ U : 5 divides x}, what is n(A′ ∪ B′)?If U = ℝ, A = [−5, 1), and B = (3, 8], what is (A ∪ B)′?If U = {1, 2, ..., 16}, A = {x ∈ U : x is a square number}, and B = {x ∈ U : x is odd}, what is A′ ∩ B?