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 U = {1,2,3,4,5,6,7} and A = {2,4,6}, how many members of P(U) are subsets of A′?If A = {1,2,3,4}, how many members of P(A) are singleton sets?If |A| = 4, how many singleton members are there in P(P(A))?If A = {1, 2, 3}, what is the truth value of the statement {{1}, {2}} ⊆ P(A)?If A = {1, 2}, which statement is correct: {1} ∈ P(A) or {1} ⊆ P(A)?Let U = {x ∈ N : 1 ≤ x ≤ 15} and A = {x ∈ U : x is divisible by 3}. What is |P(A')|?Let U = {x ∈ N : 1 ≤ x ≤ 20} and A = {x ∈ U : x is prime}. How many non-empty subsets does A' have?If A = {x ∈ Z : −2 ≤ x ≤ 3}, what is |P(A)|?Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} and A be the set of odd elements of U. How many 3-element members are there in P(A')?If A has n elements and P(A) contains 31 proper subsets, what is n?If A ⊆ U, |A| = m, and |U| = 2m, when does |P(A)| = |P(A')| hold?If A ⊆ U, |U| = 18, and |P(A′)| = 1024, what is |P(A)|?If A = {1, 2, 3, 4}, how many members does the power set P(A) have, excluding A itself?If A = {1, 2, 3, 4, 5, 6}, how many subsets in P(A) have even cardinality?If A = {1, 2, 3, 4, 5}, how many subsets in P(A) contain both 1 and 2 and do not contain 5?If A = {a, b, c, d, e}, how many subsets in P(A) contain at least one of a or b?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')|, where complements are taken with respect to U?Let U = {1,2,3,4,5,6,7,8,9}, A = {1,2,3,4,5}, and B = {4,5,6,7}. What is the cardinality of P(A' ∪ B')?If |A| = 5, how many members of the power set P(A) remain after excluding both A and the empty set?If A = {1,2,3,4} and B = {3,4,5,6}, what is |P(A ∪ B)| − |P(A ∩ B)|?