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=∅, |A|=3, and |B|=4, what is |P(A)∩P(B)|?If |A|=4, |B|=5, and |A∩B|=2, what is |P(A)∩P(B)|?If A = {1, 2} and B = {3, 4}, how many members are in P(A ∪ B) − (P(A) ∪ P(B))?If A = {p, q, r}, how many two-element subsets are members of the power set P(A)?If |A| = 6, how many members of the power set P(A) have exactly 4 elements?If A has 7 elements, how many subsets in P(A) have an odd number of elements?If |A| = 8, how many subsets in P(A) have even cardinality?If A = {1, 2, 3, 4, 5}, how many subsets in P(A) must contain 1 and must not contain 5?If A = {a, b, c, d, e, f}, how many subsets in P(A) contain both a and b?If A = {1, 2, 3, 4, 5, 6}, how many subsets in P(A) contain at least one of 2 or 4?If A = {1, 2, 3, 4}, how many subsets in P(A) contain {1, 2} as a subset?Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 3, 5, 7}, and B = {2, 3, 5, 8}. What is |P((A ∪ B)')|, where the complement is taken relative to U?If U = {x ∈ N : 1 ≤ x ≤ 12} and A = {x ∈ U : x is prime}, what is |P(A')|?If U = {1,2,3,4,5,6,7,8,9,10} and A = {x : x ∈ U, x is even}, how many non-empty members are in P(A′)?If A = {1,2}, which statement about {1} ⊆ P(A) is true?If A = {a,b,c,d}, how many subsets in P(A) do not contain a?If A = {1,2,3,4,5}, how many subsets in P(A) either contain both 2 and 3 or contain neither of them?If A = {1,2,3,4,5,6}, how many subsets in P(A) contain 1 and have even cardinality?If U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, and B = {3, 4, 5}, what is |P((A ∩ B)')|, where the complement is taken relative to U?If |U| = 10, |A| = 6, |B| = 5, and |A ∩ B| = 3, what is |P((A ∪ B)′)|?