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 = {0, 1, 2, 3}, how many elements of P(A), that is, subsets of A, have sum 3?Let U = {x : x ∈ N, x ≤ 12} and A = {x ∈ U : x is a multiple of 3}. How many elements does A' have?If A = {m, n}, which of the following is not a subset of P(A)?If A has n elements and P(A) has 64 elements, how many 3-element subsets does A have?If A = {1, 2, 3, 4, 5}, how many elements of P(A) contain both 2 and 5 but do not contain 1?If A={a,b,c,d}, how many elements of P(A) are subsets with an odd number of elements?If A={∅,0}, what is P(A)?If A has 6 elements, how many elements of P(A) do not have exactly 2 elements?If A={1,2,3,4}, how many elements of P(A) do not contain 1 and do contain 4?If A={1,2,3}, which of the following statements is false?If \(A=\{1,2,3,4,5\}\), how many subsets of the power set \(\mathcal{P}(A)\) have even cardinality?If \(A=\{a,b,c\}\), how many elements of \(\mathcal{P}(A)\) are supersets of \(\{a,b\}\)?If \(A=\{1,2,3,4\}\), how many elements of \(\mathcal{P}(A)\) contain exactly one of \(1\) and \(2\)?If \(A=\{1,2,3\}\), how many elements does \(\mathcal{P}(A)\setminus\{\varnothing,A\}\) contain?If \(A=\{x,y,z,w\}\), how many elements of \(\mathcal{P}(A)\) are disjoint from \(\{x,z\}\)?If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is the value of |P(A ∩ B)|, where P denotes the power set?If A = {a, b, c, d, e}, how many elements of P(A) contain a but do not contain both b and c?If A = {2,4,6,8,10}, how many elements of P(A) contain only even numbers?If |A| = 6, how many elements of P(A) have cardinality 2 or cardinality 4?Let A = {∅,{a},b}. Which of the following is an element of P(A)?