Assertion: ∅ ⊆ A is true for every set A. Reason: There is no element in ∅ that is not in A. Choose the correct option.
Answer and explanation
Correct answer: Both the assertion and the reason are true, and the reason correctly explains the assertion.
By definition, X ⊆ A means that every element of X is also an element of A. The empty set has no elements, so it is impossible to find an element of ∅ that lies outside A. Thus the universal condition is automatically true for every set A; this is commonly called vacuous truth. The reason states exactly why the empty set is a subset of every set, so both the assertion and reason are true and the reason correctly explains the assertion.
Frequently asked questions
What is the correct answer to this question?
Both the assertion and the reason are true, and the reason correctly explains the assertion.
Why is this the correct answer?
By definition, X ⊆ A means that every element of X is also an element of A. The empty set has no elements, so it is impossible to find an element of ∅ that lies outside A. Thus the universal condition is automatically true for every set A; this is commonly called vacuous truth. The reason states exactly why the empty set is a subset of every set, so both the assertion and reason are true and the reason correctly explains the assertion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
