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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.

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1. If U = {1, 2, ..., 22}, A = {x : x ∈ U, x is even}, and B = {x : x ∈ U, x is a perfect square}, what is (A ∩ B)'?Hard · Level 3

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{1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22}
{4, 16}
{1, 4, 9, 16}
{2, 6, 8, 10, 12, 14, 18, 20, 22}

2. If U = {1, 2, ..., 81}, A = {x : x ∈ U, 3 divides x}, and B = {x : x ∈ U, 27 divides x}, how many elements are in B' ∩ A?Hard · Level 3

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3. Let U = {x ∈ ℕ : x ≤ 120}, A = {x ∈ U : 8 divides x}, B = {x ∈ U : 15 divides x}, and C = {x ∈ U : 20 divides x}. What is n((A ∪ B ∪ C)′)?Hard · Level 3

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4. Let U = ℝ, A = {x ∈ ℝ : (x - 2)(x + 5) ≤ 0}, and B = {x ∈ ℝ : |x - 1| < 3}. What is (A′ ∩ B)′?Hard · Level 3

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(-∞, 2] ∪ [4, ∞)
(2, 4)
[-5, 2] ∪ [-2, 4]
(-∞, -5) ∪ (4, ∞)

Complement of a Set and Its Properties

Quiz this set

If U = {1, 2, ..., 22}, A = {x : x ∈ U, x is even}, and B = {x : x ∈ U, x is a perfect square}, what is (A ∩ B)'?

If U = {1, 2, ..., 81}, A = {x : x ∈ U, 3 divides x}, and B = {x : x ∈ U, 27 divides x}, how many elements are in B' ∩ A?

Let U = {x ∈ ℕ : x ≤ 120}, A = {x ∈ U : 8 divides x}, B = {x ∈ U : 15 divides x}, and C = {x ∈ U : 20 divides x}. What is n((A ∪ B ∪ C)′)?

Let U = ℝ, A = {x ∈ ℝ : (x - 2)(x + 5) ≤ 0}, and B = {x ∈ ℝ : |x - 1| < 3}. What is (A′ ∩ B)′?

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Complement of a Set and Its Properties

Quiz this set

If U = {1, 2, ..., 22}, A = {x : x ∈ U, x is even}, and B = {x : x ∈ U, x is a perfect square}, what is (A ∩ B)'?

If U = {1, 2, ..., 81}, A = {x : x ∈ U, 3 divides x}, and B = {x : x ∈ U, 27 divides x}, how many elements are in B' ∩ A?

Let U = {x ∈ ℕ : x ≤ 120}, A = {x ∈ U : 8 divides x}, B = {x ∈ U : 15 divides x}, and C = {x ∈ U : 20 divides x}. What is n((A ∪ B ∪ C)′)?

Let U = ℝ, A = {x ∈ ℝ : (x - 2)(x + 5) ≤ 0}, and B = {x ∈ ℝ : |x - 1| < 3}. What is (A′ ∩ B)′?

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