If {7} ∈ P(A), which statement is definitely true?
Answer and explanation
Correct answer: 7 ∈ A
By definition, X ∈ P(A) means that X is a subset of A. Therefore, {7} ∈ P(A) means {7} ⊆ A. Since the only element of the singleton {7} is 7, this necessarily implies 7 ∈ A. It does not imply that {7} itself is an element of A, nor that A contains no other elements. Thus option A is definitely true, while options B and C are not required and option D is false.
Frequently asked questions
What is the correct answer to this question?
7 ∈ A
Why is this the correct answer?
By definition, X ∈ P(A) means that X is a subset of A. Therefore, {7} ∈ P(A) means {7} ⊆ A. Since the only element of the singleton {7} is 7, this necessarily implies 7 ∈ A. It does not imply that {7} itself is an element of A, nor that A contains no other elements. Thus option A is definitely true, while options B and C are not required and option D is false.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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