Consider the two sets :
A = {m $\in$ R : both the roots of
x² – (m + 1)x + m + 4 = 0 are real}
and B = [–3, 5).
Which of the following is not true?

As roots are real so, $D \ge 0$<br><br>${(m + 1)^2} - 4(m + 4) \ge 0$<br><br>$\Rightarrow {m^2} - 2m - 15 \ge 0$<br><br>$\Rightarrow$ $(m - 5)(m + 3) \ge 0$<br><br>$m\, \in \,$($-$$\propto$, $-$3] $\cup$ [5, $\propto$)<br><br>$A= ( -$$\propto$, $-$3] $\cup$ [5, $\propto$)<br><br>Given B = [$-$3, 5)<br><p>Now, let&#39;s examine the options.</p> <p><b>Option A :</b> A ∩ B = {–3} The intersection of sets A and B would be the set of elements common to both sets. In this case, the only common element is -3. So, option A is true.</p> <p><b>Option B :</b> B – A = (–3, 5) The subtraction (or difference) of sets A from B is the set of elements that are in B but not in A. B is [–3, 5), and A is (-∞, -3] U [5, ∞). Subtracting A from B would leave an open interval (-3, 5), not including -3 and 5. So, option B is also true.</p> <p><b>Option C :</b> A ∪ B = R The union of sets A and B is the set of elements that are in A, or B, or both. Here, A U B would cover all real numbers. So, option C is true.</p> <p><b>Option D :</b> A - B = (-∞, -3) ∪ (5, ∞) The subtraction (or difference) of set B from A is the set of elements that are in A but not in B. B is [–3, 5), and A is (-∞, -3] U [5, ∞). Subtracting B from A would leave (-∞, -3) U [5, ∞), not including -3 and 5. But according to the convention for writing intervals, it should be (-∞, -3) U (5, ∞). So, option D is not true.</p>