For any set A, which statement is always true?
Answer and explanation
Correct answer: ∅ ⊆ A — the empty set is a subset of A
The empty set has no elements. To be a subset of A, every element of the first set must belong to A; because the empty set has no elements, there is no possible violation of this condition. Thus ∅ ⊆ A for every set A. The other statements are not always true: A may be nonempty, A need not equal ∅, and ∅ has no elements at all.
Frequently asked questions
What is the correct answer to this question?
∅ ⊆ A — the empty set is a subset of A
Why is this the correct answer?
The empty set has no elements. To be a subset of A, every element of the first set must belong to A; because the empty set has no elements, there is no possible violation of this condition. Thus ∅ ⊆ A for every set A. The other statements are not always true: A may be nonempty, A need not equal ∅, and ∅ has no elements at all.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
