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}, how many elements of P(A) must contain 1?If A={p,q,r,s}, how many elements of P(A) do not contain p?If U = {1, 2, ..., 15} and A = {3, 6, 9, 12, 15}, what is n(P(A'))?If A={1,2,{1,2}}, which statement is correct?If n(A)=5, how many elements of P(A) have at least 4 elements?If A={a,b,c}, how many subsets in P(A) have an odd number of elements?If A⊆B, which relation between P(A) and P(B) is always true?If A={1,2,3,4}, how many subsets in P(A) contain 1 but do not contain 4?If U = {a, b, c, d}, how many elements of P(U) have a singleton complement?If \(A\) is the empty set, which statement about \(\mathcal{P}(A)\) is correct?If A = {1, 2, 3, 4, 5}, how many subsets in P(A) have exactly 2 or exactly 3 elements?Let A be the set of distinct letters in the English word “sets”. What is n(P(A))?If \(U=\{0,1,2,3,4,5\}\) and \(A=\{x:x^2=x\}\), what is \(n(\mathcal{P}(A'))\)? Here, \(A'\) denotes the complement of \(A\) in \(U\).If A = {a, b, c, d, e}, how many subsets of A contain both a and b?If \(U=\{1,2,\ldots,25\}\) and \(A=\{x\in U:x\text{ is a perfect square}\}\), what is \(n(A')\)?If A = {1, 2, 3}, how many elements of P(A) are proper subsets of A?If A = {1, 2, 3, 4}, how many subsets of A contain 2 and have even size?If A = {a,b,c}, how many elements of P(A) are disjoint from A?If A = {1,2,3,4,5,6}, how many subsets in P(A) contain at least one of 1 or 2?If U = {1,2,3,4,5} and A = {1,2}, why is P(A') ⊆ P(U) true?