Mathematics
Power Set and Subsets
घात समुच्चय और उपसमुच्चय
In Class 11 Mathematics, under the chapter Sets, Power Set and Subsets explains subsets, proper subsets, and the power set of a given set. Students learn to identify whether one set is contained in another, list elements of a power set, and count subsets with specified elements or cardinalities.
Practice questions
If A = {1,2,3,4}, how many subsets in P(A) are equal to their own complement with respect to A?If A = {1,2,3,4,5}, how many subsets in P(A) contain 1 or do not contain 5?If U = {1,2,...,14}, A = {2,4,6,8,10,12,14}, and B = {1,3,5,7,9,11,13}, what is true about P(A') = P(B)?If U = {1,2,...,16}, A is the set of divisors of 16, and B = A', what is n(P(B))?If A = {∅, {1}, 2}, which one is not an element of P(A)?If \(n(\mathcal{P}(A))=32\) and \(n(U)=13\), how many 2-element subsets does \(A'\) have?Let \(U=\{1,2,\ldots,20\}\). If \(A\) is the set of multiples of 4 and \(B\) is the set of multiples of 6 in \(U\), what is \(n((A\cup B)')\)?If A = {a, b, c, d, e}, how many subsets in P(A) contain a and contain neither b nor c?If \(A=\{1,2,3,4\}\) and \(U=\{1,2,3,4,5,6\}\), how many members of \(\mathcal{P}(A)\) are subsets of \(U\)?If \(U=\{a,b,c,d,e\}\) and \(A=\{a,c,e\}\), how many members does \(\mathcal{P}(A')\) have?If \(|U|=9\), \(|A|=5\), and \(A\subseteq U\), what is the value of \(|\mathcal{P}(U-A)|\)?If \(A=\varnothing\), how many members are there in \(\mathcal{P}(\mathcal{P}(A))\)?If \(|\mathcal{P}(A)|=64\), what is the value of \(|\mathcal{P}(\mathcal{P}(A))|\)?If \(A=\{x:x\in\mathbb{N},\ x\leq5\}\) and \(U=\{x:x\in\mathbb{N},\ x\leq8\}\), how many members are in \(\mathcal{P}(U)-\mathcal{P}(A)\)?If U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, which of the following is not a member of P(A′)?If A={1,{2},3}, which of the following is a member of P(A)?If A={∅,{∅}}, what is |P(A)|?If A ⊆ U, |U| = 7, and |P(A′)| = 8, what is |A|?If A={1,2} and B={2,3}, how many proper subsets are in P(A∪B)?If U={1,2,3,4,5} and A={1,4}, what is P(A)∩P(A')?