COMEDK · Maths · 20. Sets and Relations
If \(A=\left\{x: x^{2}-x+2>0\right\}\) and \(B=\left\{x: x^{2}-4 x+3 \leq 0\right\}\), then \(A \cap B\) is
- A \([1,3]\)
- B \((-\infty, \infty)\)
- C \((1,3)\)
- D \((-\infty, 1) \cup(3, \infty)\)
Answer & Solution
Correct Answer
(A) \([1,3]\)
Step-by-step Solution
Detailed explanation
Here, \(A=\left\{x: x^{2}-x+2>0\right\}=R\) \(\left(\begin{array}{l} \because x^{2}-x+2=x^{2}-x+\frac{1}{4}+\frac{7}{4} \\ =\left(x-\frac{1}{2}\right)^{2}+\frac{7}{4} \geq \frac{7}{4} \end{array}\right)\) and \(B=\left\{x: x^{2}-4 x+3 \leq 0\right\}\)…
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