If \(A=\{x:x^2-7x+12=0\}\) and \(B=\{3,4\}\), which relation is correct?
Answer and explanation
Correct answer: \(A=B\)
To determine set \(A\), factor the quadratic equation: \(x^2-7x+12=(x-3)(x-4)=0\). Therefore, the possible values of \(x\) are \(3\) and \(4\), so \(A=\{3,4\}\). This is exactly the set given as \(B\). Since sets are equal when they contain precisely the same elements, \(A=B\). Neither set is a proper subset of the other, and their intersection is not empty; in fact, their intersection is the whole set \(\{3,4\}\).
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
To determine set \(A\), factor the quadratic equation: \(x^2-7x+12=(x-3)(x-4)=0\). Therefore, the possible values of \(x\) are \(3\) and \(4\), so \(A=\{3,4\}\). This is exactly the set given as \(B\). Since sets are equal when they contain precisely the same elements, \(A=B\). Neither set is a proper subset of the other, and their intersection is not empty; in fact, their intersection is the whole set \(\{3,4\}\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
