Consider the statement: If \(A\subset B\), then \(A\ne B\). What is the nature of this statement?
Answer and explanation
Correct answer: True
Here \(A\subset B\) is understood as a proper-subset relation: every element of \(A\) belongs to \(B\), and at least one element of \(B\) is not in \(A\). Consequently, the two sets cannot have exactly the same elements, so \(A\ne B\). This conclusion applies to finite, infinite, and empty-set examples whenever the proper-subset relation is valid. Therefore, the statement is true and option A is correct.
Frequently asked questions
What is the correct answer to this question?
True
Why is this the correct answer?
Here \(A\subset B\) is understood as a proper-subset relation: every element of \(A\) belongs to \(B\), and at least one element of \(B\) is not in \(A\). Consequently, the two sets cannot have exactly the same elements, so \(A\ne B\). This conclusion applies to finite, infinite, and empty-set examples whenever the proper-subset relation is valid. Therefore, the statement is true and 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.
