Which statement about the empty set is always true?
Answer and explanation
Correct answer: ∅ ⊆ A
The empty set ∅ is a subset of every set A. A subset relation requires every element of the first set to belong to the second set. Since ∅ has no elements, there is no element that can violate this condition; consequently, ∅ ⊆ A is always true. The other statements require additional conditions: A must be empty for A ⊆ ∅ or ∅ = A, and ∅ ∈ A depends on whether A contains the empty set as an element.
Frequently asked questions
What is the correct answer to this question?
∅ ⊆ A
Why is this the correct answer?
The empty set ∅ is a subset of every set A. A subset relation requires every element of the first set to belong to the second set. Since ∅ has no elements, there is no element that can violate this condition; consequently, ∅ ⊆ A is always true. The other statements require additional conditions: A must be empty for A ⊆ ∅ or ∅ = A, and ∅ ∈ A depends on whether A contains the empty set as an element.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
