If A = {r, s, t}, why is ∅ in P(A)?
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Answer and explanation
Correct answer: Because ∅ ⊆ A
The empty set ∅ is a subset of every set because it has no elements that could fail to belong to that set. In particular, every element of ∅ is an element of A vacuously, so ∅ ⊆ A. Since P(A) is the collection of all subsets of A, ∅ must be one of its elements. It does not mean that ∅ equals A.
Frequently asked questions
What is the correct answer to this question?
Because ∅ ⊆ A
Why is this the correct answer?
The empty set ∅ is a subset of every set because it has no elements that could fail to belong to that set. In particular, every element of ∅ is an element of A vacuously, so ∅ ⊆ A. Since P(A) is the collection of all subsets of A, ∅ must be one of its elements. It does not mean that ∅ equals A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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