If \(A=\{1,2,3\}\) and \(B\) is the set of elements of \(A\) that are less than or equal to 3, choose the correct option.
Answer and explanation
Correct answer: \(A=B\)
The elements of \(A\) are 1, 2, and 3. Each of these satisfies the condition \(x\leq 3\), so every element of \(A\) is included in \(B\). Since \(B\) is defined only using elements of \(A\), it cannot contain anything else. Thus \(B=\{1,2,3\}=A\). Neither set is a proper subset of the other, and \(B\) is certainly not empty.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The elements of \(A\) are 1, 2, and 3. Each of these satisfies the condition \(x\leq 3\), so every element of \(A\) is included in \(B\). Since \(B\) is defined only using elements of \(A\), it cannot contain anything else. Thus \(B=\{1,2,3\}=A\). Neither set is a proper subset of the other, and \(B\) is certainly not empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
