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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 = {1,2,3,4,5,6,7,8}, A = {1,2,3,4}, and B = {5,6,7,8}, what is the relation between B and A?If U = {1,2,3,4,5} and A = {1,2}, what is Aᶜ \ A?If U = {1, 2, 3, 4, 5} and A = {1, 2}, what is A \ Aᶜ?If n(Aᶜ) = 12 and n(U) = 30 for the universal set U, what is the value of n(A)?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {2, 4, 6, 8}, which statement is correct?If U = {a, b, c, d, e, f}, A = {a, b, c}, and D = {d, e, f}, which conclusion is correct using A ∩ D and A ∪ D?If U = {x : x ∈ ℕ, x ≤ 12} and A = {x ∈ U : x is not divisible by 2}, what is Aᶜ?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5, 6}, and B = {4, 5, 6, 7, 8}, what is (A \ B)ᶜ?If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 3, 4}, and B = {3, 4, 5, 6}, what is (Aᶜ ∪ B)ᶜ?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {2, 3, 5, 7}, and B = {1, 4, 6, 8, 9, 10}, which statement is correct for A and B?If U = {1, 2, 3, …, 15} and A is the set of perfect squares in U, how many elements are in Aᶜ?If U = {1, 2, 3, …, 16} and A is the set of perfect squares in U, how many elements does Aᶜ contain?If U = R and A = {x ∈ R : x ≥ 3}, what is Aᶜ?If U = {1,2,3,4,5,6,7,8,9,10,11,12}, A = {1,2,3,4,5,6}, and B = {2,4,6,8,10,12}, what is Aᶜ ∩ B?If U = {1,2,3,4,5,6,7,8,9}, A = {1,2,3,4}, B = {3,4,5,6}, and C = {5,6,7,8}, what is (A ∪ B ∪ C)ᶜ?If U = {x : x ∈ N, 1 ≤ x ≤ 30} and A = {x ∈ U : x is divisible by both 2 and 3}, what is n(Aᶜ)?If U = {1, 2, ..., 30}, A is the set of prime numbers and B is the set of multiples of 3, then how many elements are in (A ∪ B)'?If U = {x : x ∈ ℤ, −5 ≤ x ≤ 5} and A = {x : x² ≤ 9}, what is A'?If A ⊆ B ⊆ U, which relation is always true?If U is the universal set, then (A ∩ B')' is equal to which of the following?