If \(A=\{x\in\mathbb Z:x^2-4x+3=0\}\) and \(B=\{1,3\}\), which relation is correct?
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Answer and explanation
Correct answer: \(A=B\)
Solve the quadratic condition defining \(A\): \(x^2-4x+3=(x-1)(x-3)=0\). Hence the integer solutions are \(x=1\) and \(x=3\), so \(A=\{1,3\}\). This is exactly the set \(B\). The order in which elements are written does not matter in a set, and no element is repeated. Therefore, \(A=B\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
Solve the quadratic condition defining \(A\): \(x^2-4x+3=(x-1)(x-3)=0\). Hence the integer solutions are \(x=1\) and \(x=3\), so \(A=\{1,3\}\). This is exactly the set \(B\). The order in which elements are written does not matter in a set, and no element is repeated. Therefore, \(A=B\), making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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