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 the universal set is \(U=\{1,2,\ldots,32\}\) and \(A=\{x:x=2^n,\ n\in\mathbb{N},\ 0\le n\le 5\}\), what is the value of \(|A'|\)?If \(U=\{1,2,\ldots,24\}\), \(A=\{x:x\text{ is divisible by }2\}\), \(B=\{x:x\text{ is divisible by }3\}\), and \(C=\{x:x\text{ is divisible by }4\}\), what is \(|(A\cup B\cup C)'|\)?If U = ℝ, A = (1,4] and B = [4,7), what is (A ∪ B)'?If U = {1,2,...,30}, A = {x : x is a multiple of 2}, and B = {x : x is a multiple of 3}, what is the smallest element of (A ∪ B)'?If A ∩ B = ∅, what is (A ∪ B)' equal to?If U = {1,2,...,14}, A = {1,3,5,7,9,11,13} and B = {2,3,5,7,11,13}, what is A' ∩ B'?If U = ℝ and A = {x : 0 < x < 2 or 5 ≤ x < 9}, what is A'?If A' ∪ B' = U, what conclusion is correct about A ∩ B?Let U = {1,2,...,55}, A = {x ∈ U : x is divisible by 5}, and B = {x ∈ U : x is divisible by 11}. What is |A' ∩ B'|?Let U = {1, 2, ..., 21} and A = {x : x is divisible by 3}. How many odd elements are there in A′, the complement of A in U?If U = ℝ and A = {x : x² − 2x − 8 ≤ 0}, what is A'?In a class of 80 students, 46 play cricket, 38 play football, and 20 play both. How many students play neither game?If A and B are subsets of a universal set U and A is a subset of B, which of the following statements is always true?If U = {1, 2, …, 36}, A = {x : x is divisible by 2}, and B = {x : x is divisible by 3}, what is |A′ ∩ B′|?If U = ℝ and A = {x : −3 ≤ x < 4 or 7 < x ≤ 10}, what is A′?If U = {1, 2, …, 84}, A = {x : x is divisible by 6}, and B = {x : x is divisible by 14}, what is |(A ∩ B)′|?If U = {1, 2, …, 96}, A = {x : x is divisible by 6}, and B = {x : x is divisible by 8}, what is |(A ∪ B)′|?If U = {x : x ∈ ℤ, −10 ≤ x ≤ 10} and A = {x : x² − 9x + 20 ≤ 0}, what is A′?If U = ℝ, A = (−6, 1] and B = [−2, 5), what is (A ∪ B)′?If A′ ⊆ B′, which conclusion is always correct?