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 ⊆ U, |A| = 4, and |A'| = 5, what is |P(U)|?If the set U has 10 elements, how many members of P(U) are disjoint from a fixed 4-element subset of U?If A ⊆ U, |U| = 16, and |P(A)| = 256, how many non-empty subsets of A' are there?If U = {1,2,3,4,5,6,7,8,9,10,11}, A = {1,4,7,10}, and B = {2,4,6,8,10}, what is P(A ∩ B)?If A = {a,b,c,d,e,f,g}, how many 4-element subsets of P(A) contain a and do not contain b?If A = {1,2,3,4} and the universal set is U = {1,2,3,4,5,6}, what is the number of elements in P(A')?If |P(P(A))| = 256, what is the value of |A|?The universal set is U = {x : x ∈ N, 1 ≤ x ≤ 10} and A = {2,4,6,8,10}. How many singleton sets are in P(A')?If A ⊆ U, |U| = 9, and |A| = 4, what is the number of proper subsets of P(A')?If P(A) = P(B), which conclusion is correct?If A = ∅, what is P(P(A))?If U = {a, b, c, d, e}, A = {a, c}, and B = {c, d}, what is the number of elements of P((A ∪ B)')?If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 3, 4}, and B = {3, 4, 5, 6}, what is n(P(A' ∩ B'))? Here P denotes the power set.If A = {1, 2, 3, 4, 5}, how many elements of P(A) have exactly 3 elements?If A = {1, 2, 3, 4}, how many elements of P(A) contain 1 but do not contain 4?If A = {a, b, c, d}, what is the number of elements of P(A) that are not empty sets?If A = {x, y, z, w}, how many elements of P(A) are not proper subsets of A?If n(A) = 6, how many elements of P(A) are subsets with an even number of elements?If n(A) = 5, how many subsets in P(A) have an odd number of elements?If A = {1, 2, 3}, which of the following is not an element of P(A)?