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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 A ∩ Aᶜ is considered, what is its value?If A ∪ Aᶜ is considered, what is its value?If U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5}, and B = {4,5,6,7}, what is A ∩ Bᶜ?If the universal set is U = {p,q,r,s,t} and A = {p,r,t}, which of the following elements belongs to Aᶜ?If x ∈ Aᶜ, which statement is correct?If U = {1,2,3,4,5,6,7,8,9,10,11,12} and A = {x ∈ U : x is a multiple of 3}, what is Aᶜ?If U = {1,2,3,4,5,6,7,8,9} and A = {x ∈ U : x is prime}, what is the complement Aᶜ with respect to U?If U = {1,2,3,4,5,6}, A = {1,2,3}, and B = {3,4,5}, what is Aᶜ ∪ Bᶜ?If U = {1,2,3,4,5,6}, A = {1,2,4}, and B = {2,4,6}, what is Aᶜ ∩ Bᶜ?If the complement of set A with respect to the universal set U is Aᶜ = ∅, which statement about A is correct?If Aᶜ = U, which statement about A is correct?If U = {1,2,3,4,5,6,7,8} and Aᶜ = {1,4,7}, what is n(A)?If U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4}, and Aᶜ ⊆ B, which elements must at least be in B?If U = {1,2,3,4,5,6} and A = {2,3,5}, what is U \ A equal to?If the universal set is U = {1,2,3,4,5,6,7} and A = {1,4,7}, how many elements does Aᶜ ∪ A contain?If U = {1,2,3,4,5,6,7}, A = {2,4,6}, how many elements are in Aᶜ ∩ A?If U = {1,2,3,4,5,6,7,8}, A = {1,2,5,8}, and C = {3,4,6,7}, which statement is correct?If U = {x : x ∈ N, 1 ≤ x ≤ 20} and A = {x : x ∈ U, x is a factor of 20}, how many elements does the complement Aᶜ relative to U contain?If U = {1,2,3,4,5,6,7,8,9,10}, A = {1,3,5,7,9}, and B = Aᶜ, what is B?If U = {x : x ∈ Z, −3 ≤ x ≤ 3} and A = {−3,−1,1,3}, what is Aᶜ?