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 A Δ B denotes the symmetric difference of A and B, what does (A Δ B)' represent?If U = {1, 2, ..., 30}, A = {x : x is even}, and B = {x : x is prime}, what is |A' ∩ B'|?For subsets \(A\) and \(B\) of a universal set \(U\), if \(A\subseteq B\), which relation between their complements is always true?If \(A'\cap B'=A'\), which of the following conclusions is always true?If \((A\cup B')\cap(A'\cup B')=B'\), which simplification shows it correctly?If \(U=\{1,2,\ldots,84\}\), \(A=\{x:x\text{ is divisible by }12\}\), and \(B=\{x:x\text{ is divisible by }21\}\), what is \(|(A\cap B)'|\)?If U = {1, 2, …, 20}, A = {1, 4, 9, 16} and B = {3, 6, 9, 12, 15, 18}, what is A ∩ B′?If U = ℝ, A = {x : −2 < x ≤ 4} and B = {x : 1 ≤ x < 7}, what is A′ ∪ B′?If \(U'=\varnothing\), which statement about \(U\) is correct?If \(U=\{1,2,\ldots,32\}\), \(A=\{x:x\text{ is a multiple of }4\}\), and \(B=\{x:x\text{ is a multiple of }16\}\), how many elements are in \(A'\cup B\)?If \(U=\{1,2,\ldots,64\}\) and \(A=\{x:x=2^n,\ n\in\mathbb N,\ 1\le n\le6\}\), what is the cardinality \(|A'|\) of the complement of \(A\) in \(U\)?If U = {1, 2, ..., 36}, A = {x ∈ U : x is divisible by 2}, B = {x ∈ U : x is divisible by 3}, and C = {x ∈ U : x is divisible by 6}, what is |(A ∪ B ∪ C)'|?If U = R, A = [-3, 2) and B = (2, 6], what is (A ∪ B)'?If U = {1, 2, ..., 45}, A = {x : x is a multiple of 3}, and B = {x : x is a multiple of 5}, what is the greatest element of (A ∪ B)'?If A ∪ B = ∅, what is A' ∩ B' equal to?If U = {1, 2, ..., 16}, A = {1, 3, 5, 7, 9, 11, 13, 15}, and B = {1, 2, 3, 5, 8, 13}, what is A' ∩ B'?If U = R and A = {x ∈ R : −5 ≤ x < −1 or 2 < x ≤ 7}, what is A'?If A' ∩ B' = U, what is the correct conclusion about A ∪ B?If U = {1, 2, ..., 77}, A = {x ∈ U : x is divisible by 7}, and B = {x ∈ U : x is divisible by 11}, what is |A' ∩ B'|?If U = {1, 2, ..., 33} and A = {x : x is divisible by 3}, how many even elements are in A'?