Consider the statement: Every set is a subset of itself. What is its truth value?
Answer and explanation
Correct answer: True
For any set \(A\), every element of \(A\) is automatically an element of \(A\). This satisfies the definition of a subset, so \(A\subseteq A\) is always true. The statement does not depend on whether the set is empty, finite, or infinite. For the empty set, there is no element that violates the condition, so \(\varnothing\subseteq\varnothing\) is also true. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
True
Why is this the correct answer?
For any set \(A\), every element of \(A\) is automatically an element of \(A\). This satisfies the definition of a subset, so \(A\subseteq A\) is always true. The statement does not depend on whether the set is empty, finite, or infinite. For the empty set, there is no element that violates the condition, so \(\varnothing\subseteq\varnothing\) is also true. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
