If A = {1, 2, 3}, which of the following is not an element of P(A)?
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Answer and explanation
Correct answer: {{1}}
An element of P(A) must be a subset of A, so all of its elements must be 1, 2, or 3. The sets {1, 2}, ∅, and {1, 2, 3} satisfy this requirement. However, {{1}} has the single element {1}, which is itself a set and is not an element of A. Therefore {{1}} is not a subset of A and is not an element of P(A).
Frequently asked questions
What is the correct answer to this question?
{{1}}
Why is this the correct answer?
An element of P(A) must be a subset of A, so all of its elements must be 1, 2, or 3. The sets {1, 2}, ∅, and {1, 2, 3} satisfy this requirement. However, {{1}} has the single element {1}, which is itself a set and is not an element of A. Therefore {{1}} is not a subset of A and is not an element 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.
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