If A = {1, 2}, which statement is correct: {1} ∈ P(A) or {1} ⊆ P(A)?
Answer and explanation
Correct answer: Only {1} ∈ P(A)
Because {1} is a subset of A = {1, 2}, it is an element of P(A); therefore {1} ∈ P(A) is true. However, {1} ⊆ P(A) means that the element 1 itself must belong to P(A). The elements of P(A) are ∅, {1}, {2}, and {1, 2}; the number 1 is not one of them. Thus only the first statement is true, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
Only {1} ∈ P(A)
Why is this the correct answer?
Because {1} is a subset of A = {1, 2}, it is an element of P(A); therefore {1} ∈ P(A) is true. However, {1} ⊆ P(A) means that the element 1 itself must belong to P(A). The elements of P(A) are ∅, {1}, {2}, and {1, 2}; the number 1 is not one of them. Thus only the first statement is true, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
