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, ..., 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′)?If U = {x : x ∈ ℕ, x ≤ 96}, A = {x : x ∈ U, 8 divides x}, and B = {x : x ∈ U, 12 divides x}, what is n(A′ ∩ B′)?If U = {x : x ∈ ℤ, −12 ≤ x ≤ 12} and A = {x : x ∈ U, x² − 9x + 18 ≤ 0}, what is n(A′)?If U = ℝ and A = (−∞, −5) ∪ [1, 4] ∪ (9, ∞), what is A′?If A ⊆ B ⊆ C ⊆ U, which relation is always true?If U = {1, 2, ..., 42}, A is the set of multiples of 3, and B is the set of multiples of 7, what is n((A − B)′)?If U = {1, 2, ..., 40}, A is the set of multiples of 5, and B is the set of multiples of 8, what is n((A ∩ B)′)?If the universal set U = {a, b, c, d, e, f, g, i}, A = {a, c, f}, and B = {b, c, e, i}, what is the value of (A ∪ B)'?If the universal set is U = R and A = {x ∈ R : |x + 1| ≥ 4}, what is A'?Let U = {1, 2, ..., 30}, A = {x : x ∈ U and x is a perfect square}, and B = {x : x ∈ U and x is even}. What is A' ∩ B?If A ∩ B = A ∩ B', which conclusion must be true?If U = {1, 2, ..., 72}, A = {x ∈ U : 4 divides x}, B = {x ∈ U : 6 divides x}, and C = {x ∈ U : 9 divides x}, what is n((A ∪ B ∪ C)')?If U = ℝ, A = (-2, 6], and B = [0, 9), what is A' ∪ B'?If U = {1, 2, ..., 36} and A = {x : x ∈ U and x is not prime}, how many elements are in A'?If U = {x ∈ Z : -5 ≤ x ≤ 15} and A = {x ∈ U : x ≡ 2 (mod 5)}, what is n(A')?If n(U) = 300, n(A') = 120, n(B') = 150, and n(A' ∪ B') = 210, what is n(A ∪ B)?If U = {1, 2, ..., 20}, A = {x ∈ U : x ≤ 12}, and B = {x ∈ U : x is odd}, what is A' ∩ B?If A ∪ B′ = U, which of the following statements must be true?