WAEC Mathematics 2017 Paper

Concept:Identify the actual elements contained in $M$ and $N$ by applying the given inequalities carefully.Explanation:For $M$, $x$ satisfies $3 \leq x < 8$.So $M = \{3, 4, 5, 6, 7\}$.For $N$, $x$ satisfies $8 < x \leq 12$.So $N = \{9, 10, 11, 12\}$.Notice that $8$ is not included in either set because $M$ stops before $8$ and $N$ starts after $8$.Therefore, $M$ and $N$ have no common element.That is, $M \cap N = \varnothing$.Also, $M \cup N = \{3, 4, 5, 6, 7, 9, 10, 11, 12\}$, not including $8$.So the true conclusion is that $M$ and $N$ are disjoint sets.Answer:The correct statement is $M \cap N = \varnothing$, meaning $M$ and $N$ have no element in common; hence choose the option that states that $M$ and $N$ are disjoint.