If A={1,2,3}, which of the following statements is false?
Answer and explanation
Correct answer: 1∈P(A)
P(A) is the set of all subsets of A. Therefore ∅ belongs to P(A), {1,2} belongs to P(A), and A itself belongs to P(A), because all three are subsets of A. However, 1 is an element of A, not a subset of A. The corresponding singleton set {1} is a subset and would belong to P(A), but the bare number 1 does not. Hence statement C is false.
Frequently asked questions
What is the correct answer to this question?
1∈P(A)
Why is this the correct answer?
P(A) is the set of all subsets of A. Therefore ∅ belongs to P(A), {1,2} belongs to P(A), and A itself belongs to P(A), because all three are subsets of A. However, 1 is an element of A, not a subset of A. The corresponding singleton set {1} is a subset and would belong to P(A), but the bare number 1 does not. Hence statement C is false.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
