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 \(U=[-3,7]\) and \(A=(-1,4)\), what is \(A^c\)?If \(U=(-4,6]\) and \(A=[0,2]\), what is \(A^c\)?If A ⊆ B ⊆ C ⊆ U, which relation is correct for their complements?Suppose A and B are subsets of the same universal set. If Bᶜ ⊆ Aᶜ, which conclusion is correct?If n(U) = 75, n(A) = 42, n(B) = 38, and n(A ∩ B) = 20, what is n((A ∪ B)ᶜ)?If n(U) = 90, n(Aᶜ) = 35, n(Bᶜ) = 50, and n(Aᶜ ∩ Bᶜ) = 18, what is n(A ∩ B)?Let U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5}, and B = {4,5,6,7,8}. What is Aᶜ − Bᶜ?If U = {1,2,3,4,5,6,7,8,9}, A = {2,3,5,7}, and B = {1,2,3,4,5}, what is the complement of B − A with respect to U?If U = {1,2,3,…,40} and A = {x ∈ U : x is divisible by 4 or 5}, what is n(Aᶜ)?If U = {1,2,3,…,60} and A = {x ∈ U : 6 divides x}, what is n(Aᶜ)?Which set has a complement equal to the universal set U?If U = {x ∈ ℤ : −6 ≤ x ≤ 6} and A = {x ∈ U : x² = 16}, what is n(Aᶜ)?In a survey of 150 people, 85 like tea, 70 like coffee, and 40 like both tea and coffee. How many people like neither tea nor coffee?If n(U) = 96 and n(Aᶜ) = (1/3)n(U), what is the value of n(A)?Let U = {1, 2, 3, ..., 36} and A = {x ∈ U : x is a perfect square}. What is n(Aᶜ)?Let U = {1, 2, 3, ..., 20} and A = {x ∈ U : x is divisible by 4}. What is Aᶜ ∩ {x ∈ U : x is even}?Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5, 6}, and Aᶜ ⊆ B ⊆ U. Which is the smallest possible set B?Let U = {1, 2, 3, 4, 5, 6, 7} and A = {2, 4, 6}. Which set B satisfies Bᶜ = A?Let U = {a, b, c, d, e, g}, A = {a, d, g}, and B = {b, c, e}. Which statement is correct?If P ∩ Q = ∅ and P ∪ Q = U, then Pᶜ is equal to which set?