As roots are real so, $$D \ge 0$$

$${(m + 1)^2} - 4(m + 4) \ge 0$$

$$ \Rightarrow {m^2} - 2m - 15 \ge 0$$

$$ \Rightarrow $$ $$(m - 5)(m + 3) \ge 0$$

$$m\, \in \,$$($$ - $$$$ \propto $$, $$ - $$3] $$ \cup $$ [5, $$ \propto $$)

$$A= ( - $$$$ \propto $$, $$ - $$3] $$ \cup $$ [5, $$ \propto $$)

Given B = [$$ - $$3, 5)

Now, let's examine the options.

Option A : 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.

Option 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.

Option C : 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.

Option D : 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.