If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), and \(C=\{x\mid x\in A\) and \(x\) is even\}\), which statement is correct?
Answer and explanation
Correct answer: \(B=C\) और \(B\subset A\)
To form \(C\), select from \(A\) only those elements that are even. The even elements of \(\{1,2,3,4,5,6\}\) are 2, 4, and 6, so \(C=\{2,4,6\}\). This is exactly the set \(B\), hence \(B=C\). Since 2, 4, and 6 belong to \(A\), and A also contains 1, 3, and 5, B is a proper subset of A. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(B=C\) और \(B\subset A\)
Why is this the correct answer?
To form \(C\), select from \(A\) only those elements that are even. The even elements of \(\{1,2,3,4,5,6\}\) are 2, 4, and 6, so \(C=\{2,4,6\}\). This is exactly the set \(B\), hence \(B=C\). Since 2, 4, and 6 belong to \(A\), and A also contains 1, 3, and 5, B is a proper subset of A. 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.
