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 ⊆ B ⊆ U, |U| = 9, |B| = 6, and |A| = 4, what is |P(B − A)| + |P(U − B)|?If A = {1,2,3}, how many members of P(A) are themselves singleton sets?If A = {x,y,z}, how many singleton members are in P(P(A))?If A = {1, 2, 3, 4}, how many members of the power set P(A) are disjoint from {1, 2}?If U = {1, 2, 3, 4, 5, 6, 7} and A = {1, 2, 3}, how many proper subsets does A' have?If A has n elements and |P(A)| = |P(A')|, where A ⊆ U and |U| = 12, what is the value of n?If |U| = 15 and |P(A)| = 32, where A ⊆ U, what is |P(A')|?Let A = {1, 2, 3, 4, 5}. How many subsets of the power set P(A) have cardinality greater than 2?If A = {1, 2, 3, 4, 5, 6, 7}, how many subsets in P(A) have at least 5 elements?If A = {1, 2, 3, 4, 5, 6}, among the 3-element subsets in P(A), how many contain 1?Let A = {1, 2, 3, 4, 5, 6}. Among the 3-element subsets in the power set P(A), how many do not contain the element 1?If U = {a, b, c, d, e, f, g} and A = {a, c, e}, how many members of P(U) contain A as a subset?If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {2, 4, 6, 8}, how many members of P(U) are disjoint from A'?If A ⊆ U, |U| = 11, and |𝒫(A)| = 128, how many non-empty subsets of A′ are there?If U = {1,2,3,4,5,6,7,8}, A = {1,2,3,4}, and B = {3,4,5,6}, what is |𝒫((A ∩ B)′)|?If |A| = 5, how many members of 𝒫(A) contain a fixed element a ∈ A and have odd cardinality?If U = {1,2,3,4,5,6,7,8,9,10} and A = {2,3,5,7}, what is |𝒫(A′)|?If |U| = 14, A ⊆ U, and |𝒫(A)| = 64, what is the value of |𝒫(A′)|?If A = {∅, 1, {1}}, how many members are there in 𝒫(A)?If A = {a,b,c,d}, how many members of 𝒫(A) have exactly 2 elements?