WAEC Mathematics 2021 Paper

Concept:$P \cap Q$ means the set of real numbers $x$ that satisfy both inequalities at the same time.Explanation:$P = \{x : -3 < x < 1\}$, so $x$ lies between $-3$ and $1$.$Q = \{x : -1 < x < 3\}$, so $x$ lies between $-1$ and $3$.For $x$ to be in both $P$ and $Q$, the two intervals must overlap.The lower limit is the larger of $-3$ and $-1$, which is $-1$.The upper limit is the smaller of $1$ and $3$, which is $1$.Therefore, $P \cap Q = \{x : -1 < x < 1\} = (-1,1)$.Among the listed options, the only integer in this interval is $0$.Answer:$P \cap Q = \{0\}$, i.e. option A.