If A = {m, n}, which of the following is not a subset of P(A)?
Answer and explanation
Correct answer: {m, n}
For A = {m, n}, its power set is P(A) = {∅, {m}, {n}, {m, n}}. A set X is a subset of P(A) only when every element of X is itself an element of P(A). In option C, the elements are m and n, but m and n are not subsets of A and therefore are not elements of P(A). The other choices contain only valid members of P(A), or are empty. Thus option C is the only set that is not a subset of P(A).
Frequently asked questions
What is the correct answer to this question?
{m, n}
Why is this the correct answer?
For A = {m, n}, its power set is P(A) = {∅, {m}, {n}, {m, n}}. A set X is a subset of P(A) only when every element of X is itself an element of P(A). In option C, the elements are m and n, but m and n are not subsets of A and therefore are not elements of P(A). The other choices contain only valid members of P(A), or are empty. Thus option C is the only set that is not a subset of P(A).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
