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 P(A) has 256 elements, how many elements are in P(P(A))?If A = {1, 2, 3, 4, 5, 6}, how many elements of the power set P(A) contain 1 and do not contain 6?If A = {p, q, r}, how many non-empty proper subsets does A have?If A = {1, {1}, {1, 2}}, which of the following is a subset of A?If |A| = 7, how many elements of the power set P(A) have at least 6 elements?If A = {0, 1, 2, 3, 4}, how many elements of the power set P(A) contain 0 and have odd cardinality?If A = {a, b, c, d}, how many elements of the power set P(A) are not disjoint from {a, d}?If A={1,2,3,4,5}, how many elements of the power set P(A) contain at least one of 2 and 3?If P(A)=P(B), which conclusion is necessary?If A={r,s,t,u,v}, how many elements of P(A) are supersets of {r,s} but do not contain v?If A={1,2,3,4}, how many ordered pairs (X,Y) satisfy X⊆Y⊆A and Y=A?If U={1,2,3,4,5,6,7}, A={1,3,5,7}, how many elements does the power set P(A') of the complement of A with respect to U contain?If A has 4 elements and B has 5 elements with A⊂B, how many elements are in P(B)\P(A)?If A = {∅, {∅}}, how many elements does its power set P(A) contain?Let U be the set of all triangles and let E be the set of all equilateral triangles. What does the complement E′ represent?If A = {1, 2, 3, 4, 5, 6, 7}, how many elements of P(A) do not have exactly 5 elements?Let U = {1, 2, 3, ..., 30}, and let A be the set of numbers divisible by 2 or 3. What is |A′|?If A = {a, b, c, d, e}, how many elements of P(A) contain exactly one of a and b and also contain e?If A = {1, 2, 3, 4}, how many elements of P(A) have 3 as their maximum element?If A = {1, 2, {3, 4}}, which of the following must be an element of P(A)?