If A = {1, 2}, which statement is false?
Answer and explanation
Correct answer: 1 ∈ P(A)
The power set lists all subsets of A: P(A) = {∅, {1}, {2}, {1, 2}}. Membership in P(A) therefore requires an object to be a subset of A. The number 1 is an element of A, but 1 alone is not a subset; {1} is the subset. Hence 1 ∉ P(A), making option A false. The empty set and A itself are always subsets of A, so options C and D are true.
Frequently asked questions
What is the correct answer to this question?
1 ∈ P(A)
Why is this the correct answer?
The power set lists all subsets of A: P(A) = {∅, {1}, {2}, {1, 2}}. Membership in P(A) therefore requires an object to be a subset of A. The number 1 is an element of A, but 1 alone is not a subset; {1} is the subset. Hence 1 ∉ P(A), making option A false. The empty set and A itself are always subsets of A, so options C and D are true.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
