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 U = {1,2,3,4,5,6,7,8}, A = {1,2,3}, and B = {3,4,5}, what is |𝒫((A ∪ B)′)|?If 𝒫(A) = 𝒫(B), which statement is definitely true?If A ⊆ U, |U| = 9, and |A′| = 4, how many proper subsets does A have?If A = {1, 2, 3, 4, 5}, how many subsets of A contain 1 but do not contain 2?If A = {p, q, r, s, t, u}, how many subsets of A contain neither p nor q?If (|A|=7), how many subsets in (\mathcal{P}(A)) have even cardinality?If (A={1,2,3,4,5,6}), how many subsets in (\mathcal{P}(A)) have odd cardinality and contain (6)?If (A={1,{2,3},4}), which of the following is a member of (\mathcal{P}(A))?If A = ∅, how many members are there in P(P(P(A)))?If |P(P(A))| = 256, what is |A|?If (A\subseteq B), (|A|=3), and (|B|=6), what is (|\mathcal{P}(B)-\mathcal{P}(A)|)?If |A ∩ B| = 4, what is |P(A) ∩ P(B)|?If A ∩ B = ∅, |A| = 4, and |B| = 3, what is |P(A) ∪ P(B)|?If U = {1,2,3,4,5,6,7,8,9}, A = {1,3,5,7,9}, and B = {2,3,5,8}, what is |P((A − B)′)|?If A = {1,2,3,4,5,6,7}, how many subsets in P(A) have at least 6 elements?If A = {1, 2, 3, 4, 5, 6, 7, 8}, how many subsets of the power set P(A) have at most 2 elements?If A = {a,b,c,d,e}, how many subsets in P(A) contain exactly one of a and b?If A = {1,2,3,4,5,6}, how many 3-element subsets in P(A) contain 1 and do not contain 6?If A = {1,2,3,4,5}, how many subsets in P(A) are disjoint from {1,2}?If U = {a,b,c,d,e,f,g,h} and A = {a,b,c}, how many members of P(U) contain A as a subset?