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 = R and A = {x ∈ R : x² + x − 6 ≥ 0}, what is A'?If, with respect to the universal set, \(A'\cup B=B\), which of the following conclusions is correct?Let \(U=\{1,2,\ldots,60\}\), \(A=\{x\in U:x\text{ is a multiple of }6\}\), and \(B=\{x\in U:x\text{ is a multiple of }18\}\). Then \(A'\cap B'\) is equal to which of the following?Let \(U=\{1,2,\ldots,54\}\), \(A=\{x:x\text{ is divisible by }6\}\), and \(B=\{x:x\text{ is divisible by }9\}\). What is \(|A'\cup B'|\)?Let \(U=\{1,2,3,\ldots,20\}\) and \(A=\{x:x\in U\text{ and }x\text{ is prime}\}\). What is \(A'\), the complement of \(A\) with respect to \(U\)?If U = {x ∈ ℤ | −5 ≤ x ≤ 5} and A = {x ∈ U | x² < 10}, find A′, the complement of A with respect to U.For a universal set \(U\), suppose that a set \(A\) is equal to its own complement, \(A=A'\). Which statement about \(U\) must be true?Let U = {1, 2, …, 30}, A = {x ∈ U | 2 divides x}, and B = {x ∈ U | 3 divides x}. How many elements are in (A ∪ B)′?If \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\), and \(B=\{b,c,f\}\), what is \(A'\cap B'\)?If n(U) = 80, n(A) = 35, n(B) = 42, and n(A ∩ B) = 18, find n((A ∪ B)′).If the universal set is \(U=\{1,2,\ldots,12\}\), \(A=\{2,4,6,8,10,12\}\), and \(B=\{3,6,9,12\}\), what is the complement of \(A-B\) with respect to \(U\)?If \(U=\mathbb{N}\) and \(A=\{x:x\in\mathbb{N}\text{ and }x\text{ is odd}\}\), what is \(A'\) with respect to \(U\)?If the universal set is \(U=\{x:x\in\mathbb{Z},\ 0\le x\le 10\}\) and \(A=\{x:x\in U\text{ and }x^2-5x+6=0\}\), which of the following is the complement \(A'\) of \(A\) with respect to \(U\)?With respect to a universal set, which statement correctly represents De Morgan's law for three sets?If \(U=\{1,2,\ldots,50\}\) and \(A=\{x\in U:5\mid x\}\), what is the value of \(n(A')\)?If \(A'=B'\), which conclusion is necessarily true?If the universal set is \(U=\mathbb{R}\) and \(A=\{x\in\mathbb{R}:x^2\ge 9\}\), what is \(A'\)?If \(U=\{1,2,\ldots,100\}\), \(A\) is the set of multiples of 4, and \(B\) is the set of multiples of 6, what is \(n((A\cap B)')\)?If \(A\cup A'=U\) and \(A\cap A'=\varnothing\), what is the correct meaning of \(A'\)?If \(U=\{x:x\in\mathbb{N},x\le25\}\) and \(A=\{x:x\in U\text{ and }x\text{ is a square number}\}\), how many elements are in \(A'\)?