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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 = U, n(A) = 27, and n(Aᶜ) = 33, what is n(U)?Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 2, 3, 4, 5, 6}. What is (Aᶜ)ᶜ ∩ {3, 6, 9}?If U={1,2,3,...,12} and A={3,6,9,12}, how many elements are in A^c ∪ {6,12}?Which of the following statements about the complement of a set, with respect to a universal set, is always true?If U = {x : x is a digit} and A = {x : x is a prime digit}, what is n(Aᶜ)?If U={1,2,3,...,18} and A={x:x is divisible by both 2 and 5}, what is A^c?If the universal set is U={1,2,3,...,10}, A={2,4,6,8,10}, and C=A^c, what is the value of C^c∩{1,2,3,4}?Which statement proves that A and A^c together form a partition of U?If U ≠ ∅, which statement about A = Aᶜ is correct?If U is enlarged and A remains the same, what may happen to A^c?If U1={1,2,3,4,5}, U2={1,2,3,4,5,6,7}, and A={2,5}, which extra elements are in A^c relative to U2 compared with A^c relative to U1?Given U = {1, 2, 3, ..., 12}, A = {1, 2, 3, 4}, and B = {3, 4, 5, 6, 7}, what is (Aᶜ ∩ B)ᶜ?If the universal set is U = {1,2,3,...,10}, A = {2,4,6,8,10}, and B = {1,2,3,4,5}, what is (Aᶜ ∪ B)ᶜ?If U = {1,2,3,...,24}, A is the set of elements divisible by 4, and B is the set of elements divisible by 6, how many elements are in Aᶜ ∩ Bᶜ?For subsets A and B of a universal set U, which of the following statements is always true?If U={1,2,3,...,11}, A={1,4,7,10}, and B={2,4,6,8,10}, what is A^c ∩ B^c?Which of the following statements about the complement Aᶜ of a set A is always true?If n(U) = 84 and n(A) = 2n(Aᶜ), where U is the universal set, what is n(Aᶜ)?For the universal set U, if n(U)=72 and n(A^c)=3n(A), what is the value of n(A)?If Aᶜ = {x | x ∈ U and x ∉ A}, why does A ∪ Aᶜ = U hold?