If A = {2,4,6}, what is the relation of ∅ with P(A)?
Answer and explanation
Correct answer: ∅ ∈ P(A)
The empty set is a subset of every set, including A = {2,4,6}. Since P(A) is the set of all subsets of A, the empty set must be one of its elements. Therefore ∅ ∈ P(A). It is important to distinguish the statements ∅ ⊆ A and ∅ ∈ P(A): the first says it is a subset of A, while the second says it is an element of the power set. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
∅ ∈ P(A)
Why is this the correct answer?
The empty set is a subset of every set, including A = {2,4,6}. Since P(A) is the set of all subsets of A, the empty set must be one of its elements. Therefore ∅ ∈ P(A). It is important to distinguish the statements ∅ ⊆ A and ∅ ∈ P(A): the first says it is a subset of A, while the second says it is an element of the power set. 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.
