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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

The universal set is U={m,n,o,p,q,r,s,t} and A={m,o,q,s}. What is Aᶜ?If n(U)=160 and n(A∪B∪C)=127, how many elements belong to none of the three sets?If n(Aᶜ) = 58 and n(U) = 132, what is n(A)?In three sets, only A=23, only B=27, only C=21, only A∩B=13, only B∩C=11, only C∩A=9, and A∩B∩C=7. What is n((A∪B∪C)ᶜ) if n(U)=130?By De Morgan’s law, what is \((A\cap B\cap C)^c\) equal to?By De Morgan’s law, what is (A∪B∪C)ᶜ equal to?If n(A) = 90, n(B) = 85, n(A ∪ B) = 125, and n(U) = 160, what is n(Aᶜ ∩ Bᶜ)?If n(U) = 170, n(A ∩ B) = 44, and n(Aᶜ ∪ Bᶜ) = 146, what can be said about the given data?If n(A − B) = 36, n(B − A) = 28, n(A ∩ B) = 22, and n(U) = 120, what is n(Aᶜ ∪ Bᶜ)?If A ⊆ B, n(A) = 46, n(B) = 108, and n(U) = 150, what is n(Bᶜ)?If n(U)=210, n(A∩B)=52, and n(Aᶜ∪Bᶜ)=170, what can be said about the given data?If n(A−B)=44, n(B−A)=36, n(A∩B)=29, and n(U)=150, what is n(Aᶜ∪Bᶜ)?If n(U) = 150 and n(A ∪ B) = 118, what is the number of elements in (A ∪ B)ᶜ?If n(A′) = 35, n(B′) = 42, n(U) = 80, and n(A ∩ B) = 25, what is n(A′ ∩ B′)?If A ∩ B = ∅, n(A) = 57, n(B) = 46, and n(U) = 125, what is n((A ∪ B)′)?If U = {1, 2, ..., 120}, A is the set of multiples of 8 and B is the set of multiples of 12, what is n((A ∪ B)')?If U = {1, 2, ..., 120}, A is the set of multiples of 8 and B is the set of multiples of 12, choose the correct value of n((A ∪ B)').If A, B and C are mutually disjoint, n(A)=27, n(B)=34, n(C)=41 and n(U)=125, what is n((A∪B∪C)′)?If A⊆B⊆C⊆U, then what is (A∪B∪C)′ equal to?Assertion: (A∪B)′=A′∩B′. Reason: To be outside A∪B, an element must be outside both A and B. Choose the correct option.