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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 ⊆ B, which relation is correct for their complements?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 4, 6, 8, 10}, what is Aᶜ?If U = {a, e, i, k, m} and A = {a, e, i}, what is Aᶜ?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {2, 3, 5, 7}, what is Aᶜ?According to De Morgan's law, what is (A ∪ B)ᶜ equal to?If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4\}\), what is \((A\cup B)^c\)?If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4\}\), what is \((A\cap B)^c\)?If \(U=\{0,1,2,3,4\}\) and \(A=\{0,2,4\}\), find \(A^c\).If \(U=\{1,2,3,4\}\) and \(A=\{1,4\}\), which statement is correct?Which of the following statements is always true for any set A contained in a universal set U?If \(A^c=\varnothing\), then A is equal to what?If \(A^c = U\), then what is \(A\) equal to?In a Venn diagram, the rectangle represents U and the circle represents A. What is the region outside the circle but inside the rectangle called?If \(U=\{x:x\text{ is an alphabet letter}\}\) and \(A=\{x:x\text{ is a vowel}\}\), what does \(A^c\) represent?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} and A = {3, 6, 9, 12}, what is the complement Aᶜ of A with respect to U?If n(U) = 30 and n(Aᶜ) = 18, what is n(A)?If n(U) = 16 and n(A) = n(Aᶜ), what is n(A)?Which pair of sets is always disjoint?If n(U) = 25, what is n(A ∪ Aᶜ)?For any set A, what is n(A ∩ Aᶜ)?