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 = {1,2,3,4,5,6,7,8} and A = {1,3,5,7}, how many elements of P(A′) contain only even numbers?Let A = {1,2,3}. Which statement is correct: {1} ∈ P(A) or {1} ⊆ P(A)?If A = {1,{2}}, which of the following is an element of P(A)?If A = {1,2,3}, how many elements are in P(A) − {∅, A}?If U = {1,2,3,4,5}, A = {1,2}, and B = {2,3,4}, what is n(P((A ∩ B)′))?If U = {1,2,3,4,5,6}, A = {1,2,3}, and B = {3,4,5}, what is n(P(A′ ∪ B′))?If A has 3 elements, how many elements are in P(P(P(A)))?If A = {1,2,3,4}, how many elements of P(A) contain 1 or have size 2?If A = {a,b,c,d}, how many elements of P(A) do not contain a and have odd size?If A = {1,2,3,4,5}, how many elements of P(A) do not contain 1 and must contain 2?If A is a subset of B, n(A) = 3, and n(B) = 5, how many elements does the set P(B) − P(A) contain? Here, P(X) denotes the power set of X.If U = {1, 2, 3, 4, 5, 6, 7} and A = {2, 4, 6}, how many subsets of P(A′) contain both 1 and 7?If A = {1, 2, 3, 4}, how many elements of P(A) are disjoint from A?Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {x : x ∈ U and x is even}. How many elements of P(A′) have exactly two elements?If n(A ∪ B) = 98 and n(A ∩ B) = 35, what is the value of n(A − B) + n(B − A)?If n(A) = 64, n(B) = 53, and n(A ∩ B) = 22, what is n(A' ∩ B)?If \(A\cap B=\varnothing\), \(n(A)=3\), and \(n(B)=5\), what is \(n(A\cup B)\)?If \(A=\{1,2,3\}\) and \(B=\{3,4\}\), how many elements does \(\mathcal{P}(A\cap B)\) contain?If A = {-1, 0, 1, 2} and B = {0, 1, 2}, how many ordered pairs (x, y) in A × B satisfy x + y = 1?