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,...,20} and A′ = {2,3,5,7,11,13,17,19}, what is the set A?If A \ B = ∅, which of the following statements must always be true?Let U = {1, 2, ..., 54}, A = {x ∈ U : 9 divides x}, and B = {x ∈ U : 6 divides x}. What is n(A′ ∩ B′)?If U = ℝ and A = {x ∈ ℝ : x ≤ −1 or x > 3}, what is A′?If A ⊆ B for sets A and B in a universal set U, which statement about their complements is correct?If U = {1,2,...,22} and A = {x ∈ U : x is prime}, how many odd numbers are in A′?If U={1,2,…,14} and A={2,4,6,8,10,12,14}, how many ordered pairs are in A′×A?Let U = {x ∈ ℤ | −4 ≤ x ≤ 6} and A = {x ∈ U | (x − 1)(x + 2) ≥ 0}. What is A′, the complement of A with respect to U?For a universal set U, if n(U)=200, n(A′)=76, n(B′)=89, and n(A′∩B′)=31, what is n((A∩B)′)?If the universal set U = {1, 2, 3, ..., 10}, A = {1, 2, 3}, and B = {3, 4, 5}, what is (A′ ∩ B)′, where complements are taken with respect to U?If U=R, A=[1,∞), and B=(−∞,4), what is A′∪B′?Let U = {1, 2, ..., 81} and A = {x ∈ U | x is a perfect square}. How many numbers divisible by 9 belong to A′?If U={1,2,…,18} and A is the set of primes in U, which set of multiples of 3 lies in A′?Let U = {x ∈ ℤ | 1 ≤ x ≤ 30} and A = {x ∈ U | x ≡ 1 (mod 4)}. What is n(A′), the number of elements in the complement of A with respect to U?If A⊆U, what is (A′∪A)′ equal to?If U = {1, 2, ..., 24}, A = {x ∈ U | 4 divides x}, and B = {x ∈ U | 8 divides x}, what is B′ ∩ A?If U = ℝ and A = {x ∈ ℝ : x ≠ −2 and x ≠ 5}, what is A′?If U = {1, 2, ..., 27} and A = {x : x ∈ U, 3 divides x}, how many elements divisible by 2 are in A′?Which of the following statements about the complements of two sets, relative to a universal set, is always true?If U = {x : x ∈ ℕ, x ≤ 84}, A = {x : x ∈ U, 6 divides x}, and B = {x : x ∈ U, 14 divides x}, what is n(A′ ∩ B′)?