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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={1,2,3,4,5,6,7}, A={1,2,4}, and B={2,4,6}, what is (A∩B)'?If U={1,2,...,12}, A={2,4,6,8,10,12}, and B={3,6,9,12}, how many elements are in (A∪B)'?If U is the set of students, A is the set of students studying Mathematics, and B is the set of students studying Physics, what does A'∩B' represent?If U={1,2,3,4,5} and A=∅, what is A'?If the universal set is \(U=\{a,b,c,d,e,f\}\) and \(A'=\{b,d,f\}\), what is the set \(A\)?If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{1,4,9\}\), which description correctly identifies \(A'\)?If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5,6\}\), what is \(A'\cup B'\)?Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {x ∈ U : x is divisible by neither 2 nor 5}. What is A′, the complement of A in U?Let U = {x ∈ N : x ≤ 15} and A = {x ∈ U : x is not prime}. What is A′, the complement of A in U?Let U = {1,2,3,…,12} and A = {x ∈ U : x is divisible by 4}. What is the complement A′ of A with respect to U?Let U = Z and A = {x ∈ Z : −2 ≤ x ≤ 3}. Which is the correct description of A′?If U = {a, b, c, d, e, g, h}, A = {a, c, g}, and B = {b, c, h}, what is (A ∪ B)' with respect to U?If A ⊆ U and A' = U, which statement about A is correct?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, and B = {4, 5, 6}, what is A' ∩ B, where the complement is taken with respect to U?If U is the set of all lowercase English letters and V = {a, e, i, o, u}, how many elements does the complement V' contain?If U={1,2,3,4,5,6,7,8}, A={2,4,6,8}, and B={1,2,3,4}, what is the value of (A∩B)'?Let N={1,2,3,...}. If U={x∈N:x≤20} and A={x∈U:x is a perfect square}, what is the value of |A'|?If U={0,1,2,3,4,5,6,7,8,9} and A={x∈U:x^2<25}, what is the complement A' with respect to U?Let U = {x ∈ Z : −5 ≤ x ≤ 5} and A = {x ∈ U : |x| ≤ 2}. How many elements does the complement A′ relative to U contain?If U = {1,2,3,4,5,6,7,8,9} and A = {x : x ∈ U and x is not divisible by 2}, what is A′?