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 \(U=\{1,2,\ldots,10\}\) and \(A=\{1,3,5,7,9\}\), what is \((A')'\)?Which option gives the correct form of \((A\cup B)'\)?For subsets \(A\) and \(B\) of a universal set \(U\), which of the following statements is always true?If \(U=\mathbb{R}\) and \(A=[-2,4)\), what is \(A'\)?If \(n(U)=120\) and \(n(A')=47\), what is \(n(A)\)?If \(A\cap B=\varnothing\), which statement about \(B\) must be true?If the universal set is \(U=\{1,2,\ldots,24\}\), \(A=\{x:x\in U\text{ and }x\text{ is even}\}\), and \(B=\{x:x\in U\text{ and }x\text{ is odd}\}\), what is the relation between \(A'\) and \(B\)?If \(U=\{1,2,\ldots,40\}\), \(A=\{x:x\in U\text{ and }2\mid x\}\), and \(B=\{x:x\in U\text{ and }5\mid x\}\), what is \(n(A'\cap B')\)?If \(U=\{x\in\mathbb{Z}\mid -3\le x\le 7\}\) and \(A=\{x\in U\mid x+2>4\}\), what is \(A'\), the complement of \(A\) in \(U\)?If \(A-B=A\cap B'\), then what is \((A-B)'\) equal to?If U = R, A = (-infinity, 1), and B = (4, infinity), what is (A union B)'?Which statement is false for the complement of A?Let U = {1, 2, 3, ..., 16} and A = {x in U : x is divisible by 4}. What is the complement A' with respect to U?If A is a subset of U, what is (U minus A)' equal to, where complements are taken with respect to U?Let U = {x in N : x <= 60}, A = {multiples of 3 in U}, and B = {multiples of 4 in U}. What is n((A intersection B)')?If U = {1, 2, ..., 8}, A = {1, 2, 5}, and B = {2, 4, 6}, what is A' ∪ B', where the complement is taken with respect to U?If U = R and A = {x in R : -1 < x <= 6}, what is A'?If U = {1, 2, ..., 25} and A is the set of non-prime elements of U, what is A'?Let A and B be subsets of U with A union B = U. Which statement about A' is always true?If U = {1, 2, ..., 12} and A = {1, 2, 3, 4, 5}, what is A' union A?