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 \(|U|=180\), \(|A|=85\), \(|B'|=110\), and \(|A\cap B|=28\), what is the value of \(|(A\cup B)'|\)?If U = {1, 2, …, 49}, A = {x : x is a perfect square}, and B = {x : x is odd}, what is |A′ ∩ B|?What is (A ∪ B′)′ equal to?If U = ℝ and A = {x : |x + 2| ≤ 6}, what is A′?If A ∩ B = U, what is A′ ∪ B′?If U = {1, 2, …, 120}, and A, B, C are respectively the sets of multiples of 4, 6, and 10, what is |(A ∪ B ∪ C)′|?If U = {p, q, r, s, t, u, v, w}, A′ = {q, s, w}, and B′ = {p, s, u}, what is (A ∪ B)′?If U = {1, 2, …, 36}, A is the set of multiples of 4 and B is the set of perfect squares, which element belongs to A′ ∩ B′?If B − A = B, which conclusion is always correct?If the universal set is U = ℝ and A = {x ∈ ℝ : x < −4 or x ≥ 2}, what is A′?If A ⊆ B and B′ ⊆ C, which statement about A′ is always true?If |U| = 90, |A ∩ B| = 24, |A′ ∩ B| = 17, and |A′ ∩ B′| = 29, what is |A ∩ B′|?If the universal set is U = {1, 2, ..., 42}, A = {x ∈ U : x is divisible by 3}, and B = {x ∈ U : x is divisible by 7}, what is |A' ∪ B'|?If the universal set is U = R and A = (-∞, -1) ∪ [3, 8), what is A'?If U ≠ ∅, which statement cannot always be true?If U = {1, 2, ..., 70}, A = {x : x is divisible by 5}, and B = {x : x is divisible by 7}, what is |A' ∩ B|?If U = {1, 2, …, 24} and A′ = {1, 5, 7, 11, 13, 17, 19, 23}, how many elements are in A?If U = R and A = {x : x² − 4x − 12 < 0}, what is A'?If U = {1, 2, ..., 18}, A = {2, 4, 6, 8, 10, 12}, and B = {6, 9, 12, 15, 18}, what is (B − A)'?If U = {1, 2, …, 144} and A = {x : x is not divisible by 12}, what is |A′|?