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 = {∅, {1}}, then what is n(P(A))?If A = {∅, {∅}}, which element must belong to P(A)?If U = {x ∈ Z : −2 ≤ x ≤ 2} and A = {x ∈ U : x² = 1}, then what is n(P(A′))?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {x ∈ U : x is prime}, how many elements are in P(A′)?If A has 4 elements, what is the number of 2-element subsets of P(A)?If n(P(A)) = n(P(B)), which conclusion is definitely true?If A = {1,2} and B = {3,4}, then what is P(A) ∩ P(B)?In general, P(A) ∩ P(B) is equal to which of the following?Which statement is generally false?If A = {1, 2} and B = {2, 3}, how many elements are in P(A) ∪ P(B)?Let U = {1, 2, 3, 4, 5, 6} be the universal set and A = {1, 2, 3}. What is P(A′) ∩ P(A), where A′ is the complement of A in U?If U is the universal set and A ⊆ U, why is P(A) ⊆ P(U) true?If A ⊆ U, n(U) = 7, and n(P(A)) = 16, what is n(P(A′))?If n(P(A′)) = 64 and the universal set U has n(U) = 10, what is n(A)?Which condition is required for P(A′) = P(A), where the complement is taken with respect to U?If A = {1,2,3,4,5,6}, how many elements of P(A) are subsets containing at least 2 elements?If A = {1,2,3,4,5}, how many elements of P(A) have at most 2 elements?If A = {a,b,c,d,e}, how many elements of P(A) contain both a and b?If A = {a,b,c,d,e}, how many elements of P(A) contain at least one of a or b?If A = {1,2,3,4}, how many elements of P(A) have an even sum of elements?