Assertion: If A = B, then A ⊆ B. Reason: Equal sets have exactly the same elements. Choose the correct option.
Answer and explanation
Correct answer: Both the assertion and the reason are true, and the reason correctly explains the assertion.
Equality of sets means that A and B contain exactly the same elements. Therefore, every element of A is necessarily an element of B, which is precisely the definition of A ⊆ B. The assertion is consequently true. The reason is also true because identical membership is what set equality means, and it directly explains why the subset relation follows. In fact, if A = B, then both A ⊆ B and B ⊆ A hold.
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?
Equality of sets means that A and B contain exactly the same elements. Therefore, every element of A is necessarily an element of B, which is precisely the definition of A ⊆ B. The assertion is consequently true. The reason is also true because identical membership is what set equality means, and it directly explains why the subset relation follows. In fact, if A = B, then both A ⊆ B and B ⊆ A hold.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
