Let A = {1,2,3}. Which statement is correct: {1} ∈ P(A) or {1} ⊆ P(A)?
Answer and explanation
Correct answer: Only {1} ∈ P(A) is correct
The power set P(A) consists of all subsets of A. Because {1} is a subset of A, it is an element of P(A), so {1} ∈ P(A) is true. For {1} ⊆ P(A) to be true, the element 1 itself would have to belong to P(A). However, P(A) contains sets such as ∅, {1}, and {1,2}, not the number 1 as an individual element. Hence only the first statement is correct.
Frequently asked questions
What is the correct answer to this question?
Only {1} ∈ P(A) is correct
Why is this the correct answer?
The power set P(A) consists of all subsets of A. Because {1} is a subset of A, it is an element of P(A), so {1} ∈ P(A) is true. For {1} ⊆ P(A) to be true, the element 1 itself would have to belong to P(A). However, P(A) contains sets such as ∅, {1}, and {1,2}, not the number 1 as an individual element. Hence only the first statement is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
