Which statement about the empty set is correct for every set A?
Answer and explanation
Correct answer: ∅ ⊆ A
The empty set has no elements. The statement ∅ ⊆ A means that every element of ∅ is also an element of A. Because there are no elements in ∅, there is no counterexample to this requirement; therefore the statement is true for every set A. In contrast, A ⊆ ∅ is true only when A itself is empty, and ∅ = A is not always true. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
∅ ⊆ A
Why is this the correct answer?
The empty set has no elements. The statement ∅ ⊆ A means that every element of ∅ is also an element of A. Because there are no elements in ∅, there is no counterexample to this requirement; therefore the statement is true for every set A. In contrast, A ⊆ ∅ is true only when A itself is empty, and ∅ = A is not always true. Hence option A is correct.
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.
