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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} is the universal set, what is U′?If U = {a, b, c, e} and A = {a, b, c, d}, what issue arises before finding A′ with respect to U?If U = {1, 2, 3, 4, 5, 6} and A = {1, 2}, what is n(A′), the number of elements in the complement of A?If U = {1, 2, 3, 4, 5, 6, 7} and A = {3, 5, 7}, what is the smallest number in A′?If U is the set of all days of the week and A = {Monday, Wednesday, Friday}, how many days are in A′?The universal set U contains 50 students. If n(A) = 18, n(B) = 22, and n(A ∩ B) = 7, how many students are outside A ∪ B?If A ⊆ U and A′ = ∅, what is the correct conclusion?If the universal set U = {a, b, c, d, e} and A = {b, d}, what is A′?If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {1, 3, 5, 7}, how many elements are in A′?If A is a subset of the universal set U, what is (A′)′?If A ⊆ U and A′ = U, what is A?If the universal set U has 35 elements and set A has 12 elements, how many elements does the complement A′ contain?If A is a subset of U, n(U) = 60, n(A) = 28, and n(A') = x, what is x?If U = {x ∈ N : x ≤ 12} and A = {x ∈ U : 3 divides x}, what is A'?Let U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, and B = {3, 4, 5}. What is A' ∩ B'?If U = {a, b, c, d}, A = {a, b}, and B = {b, c}, what is (A ∩ B)'?If U = {1,2,3,4,5,6,7,8,9}, A = {1,4,7}, and B = {2,4,8}, what is (A ∪ B)'?If U = {x : x ∈ ℕ, x ≤ 20} and A is the set of positive divisors of 20, what is n(A′)?If U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set and A = {2, 3, 5, 7}, what is the complement A′ of A?If U = {x ∈ N : x ≤ 15} and A = {x : x is a multiple of 5}, what is n(A′)?