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Consider the two sets:
$A = \{m \in R : both the roots of x^{2} - (m + 1) x + m + 4 = 0 are real\} and B = [- 3, 5)$ Which of the following is not true?

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$A \cup B = R$

$A \cap B = \{- 3\}$

$A - B = (- \infty, - 3) \cup (5, \infty)$

$B - A = (- 3, 5)$

answer is C.

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Detailed Solution

$\begin{array}{l} x^{2} - (m + 1) x + (m + 4) = 0 \\ Roots are real \Rightarrow Δ \geq 0 \\ \Rightarrow A = (- \infty, - 3] \cup [5, \infty) \end{array}$

$\begin{array}{l} B = [- 3, 5) \\ A - B = (- \infty, - 3) \cup [5, \infty) \\ ∴ option 3 is wrong \end{array}$

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