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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

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′?If A is a subset of the universal set U, which statement is always true for A and its complement A′?If A ⊆ B ⊆ U, what can be said about B′ ⊆ A′?If A ⊆ U, which statement about A′ ⊆ U is correct?If U = {1, 2, 3, 4, 5, 6} and A′ = {1, 6}, what is A ∪ A′?If U = {1, 2, 3, 4, 5} and A′ = {2, 5}, what is A ∩ A′?If U = {x ∈ N : 1 ≤ x ≤ 10} and P = {2, 3, 5, 7}, what is P′?If U = {x : x ∈ N, x ≤ 9} and S = {1, 4, 9}, what is S′?If U = {red, blue, green, yellow} and C = {red, green}, what is C′?If U = {x ∈ N : x ≤ 15} and M = {5, 10, 15}, how many elements are in M′?If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {1, 2, 7, 8}, which set is A′ ∪ A?If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {3, 4, 5, 6}, which set is A′ ∩ A?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4, 5}, and B = {4, 5, 6, 7}, what is (A ∪ B)′?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 5, 7, 9}, and B = {2, 3, 5, 8}, what is (A ∩ B)′?If the universal set U = {1, 2, 3, 4, 5, 6} and A = {2, 4}, what is A′ − A?If the universal set U = {1, 2, 3, 4, 5, 6} and A = {1, 5, 6}, what is A − A′?If U = {1,2,3,4,5,6,7,8,9,10} and A = {x ∈ U : x is a multiple of 2}, what is A′?If U = {x : x ∈ ℕ, 1 ≤ x ≤ 20} and A = {x ∈ U : x > 12}, what is n(A′)?