If A = {1, 2, 3} and B = P(A), which of the following is not an element of B?
Answer and explanation
Correct answer: 2
The power set P(A) is the set of all subsets of A. Therefore it contains ∅, {1, 2}, {3}, {1}, {2}, {1, 3}, {2, 3}, and {1, 2, 3}. The number 2 by itself is an element of A, but it is not a subset of A. The singleton subset containing 2 would be {2}, which is different from 2. Hence 2 is not an element of B, so option D is correct.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The power set P(A) is the set of all subsets of A. Therefore it contains ∅, {1, 2}, {3}, {1}, {2}, {1, 3}, {2, 3}, and {1, 2, 3}. The number 2 by itself is an element of A, but it is not a subset of A. The singleton subset containing 2 would be {2}, which is different from 2. Hence 2 is not an element of B, so option D is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
