Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects

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, ..., 45}, A = {x ∈ U : 3 divides x}, and B = {x ∈ U : 5 divides x}, what is n(A′ ∪ B′)?If U = ℝ, A = [−5, 1), and B = (3, 8], what is (A ∪ B)′?If U = {1, 2, ..., 16}, A = {x ∈ U : x is a square number}, and B = {x ∈ U : x is odd}, what is A′ ∩ B?If, with respect to a universal set, a set A satisfies A = A′, which statement about A is correct?If U = {1, 2, ..., 25} and A = {x ∈ U : 5 is a divisor of x}, how many prime numbers are in A′?If U = {1, 2, ..., 70}, A = {x ∈ U : 2 divides x}, and B = {x ∈ U : 7 divides x}, what is n((A − B)′)?If the universal set is U = ℝ and A = {x ∈ ℝ : x² − 6x + 8 > 0}, what is A′?If U = {1, 2, ..., 18}, A = {2, 4, 6, 8, 10, 12, 14, 16, 18}, and B = {3, 6, 9, 12, 15, 18}, what is A′ ∪ B′?If U = {x : x ∈ ℕ, x ≤ 40}, A = {x ∈ U : x is even}, and B = {x ∈ U : x is a square number}, what is n(A′ ∩ B′)?If the universal set U = {p, q, r, s, t, u, v}, A' = {q, s, u}, and B = {p, q, t, v}, what is A ∩ B?If the universal set is U = ℝ, A = (−3, ∞), and B = (−∞, 5], what is (A ∩ B)'?If U = {1, 2, …, 90}, A = {x ∈ U : 6 divides x}, and B = {x ∈ U : 10 divides x}, what is n((A ∩ B)')?If U = {1, 2, …, 12} and A = {1, 4, 7, 10}, what is A' ∩ {2, 4, 6, 8, 10, 12}?For subsets A and B of a universal set U, if A ⊆ B, which relation between their complements is correct?If U = {x ∈ ℤ : 0 ≤ x ≤ 20} and A = {x ∈ U : x² − 9x + 20 = 0}, how many elements of A' are less than 5?If U = {1, 2, …, 100} and A = {x ∈ U : 8 divides x}, what is n(A')?If the universal set is U = ℝ and A = {x ∈ ℝ : |x − 2| < 5}, what is A'?If U = {1, 2, …, 50} and A = {x ∈ U : x is not even}, what is A'?If U = {1, 2, …, 36}, A = {x ∈ U : 2 divides x}, and B = {x ∈ U : 3 divides x}, what is n(A' ∩ B)?If A ∪ B = U and A ∩ B = ∅, what is B equal to?