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 \(n(U)=31\) for the universal set \(U\), what is the value of \(n(A\cup A^c)\)?If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A^c=\{2,4,6,8\}\), what is the value of \(A\cap A^c\)?If the universal set U = {a, b, c, d, e} and the complement of A is Aᶜ = {b, e}, what is the value of A ∪ Aᶜ?If 6 ∈ U and 6 ∉ A, which conclusion is correct?If 5 ∉ Aᶜ and 5 ∈ U, which statement is correct?If the universal set U = [1, 9] and A = [1, 5), what is Aᶜ with respect to U?If the universal set U = (-3, 4] and A = (-3, 1], what is the complement Aᶜ of A with respect to U?If the universal set U = {x ∈ ℤ | -2 ≤ x ≤ 3} and A = {-1, 0, 1}, what is Aᶜ?If the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 3, 5, 7}, which of the following elements belongs to Aᶜ?If the universal set is U = {1, 2, 3, 4, 5} and A = {2, 5}, which of the following statements is correct?If the universal set U = {north, south, east, west} and A = {north, south}, what is Aᶜ?If the universal set U contains 60 students and set A contains 18 students who learn music, how many students do not learn music?If in a class n(U) = 45 and n(A) = 28, what does n(Aᶜ) mean?If A is a proper subset of the universal set U, which statement is correct?If A = {2, 4}, U₁ = {1, 2, 3, 4}, and U₂ = {1, 2, 3, 4, 5}, why can Aᶜ have two different values?What is the best test to check whether a given set B is the complement of A?If U = {10, 11, 12, 13, 14, 15} and A = {11, 13, 15}, what is the complement Aᶜ of A with respect to U?If U = {1, 2, 3, ..., 15} and A is the set of elements of U that are multiples of 5, what is Aᶜ?If U = {a, e, i, o, u, b, c, d} and A = {a, e, i, o, u}, what is Aᶜ?If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 7}, and B = {2, 3, 8}, what is (A ∪ B)ᶜ?