WAEC 2020 · Paper 2 · Q1

(a)
Consider the statements:

$p$ : Some teachers in a school are graduates. $q$ : Only graduate teachers received National honours.

(i) Represent this information in a Venn diagram. (ii) If Mr. Sowah is a teacher in the school, determine whether or not the following conclusions are valid or not valid. (I) Mr. Sowah is a graduate ⇒ Mr. Sowah received National honours. (II) Mr. Sowah received National honours ⇒ Mr. Sowah is a graduate. (III) Mr. Sowah did not receive a National honour ⇒ Mr. Sowah is not a graduate.
Model answer
$U$ = teachers in the school, $G$ = graduate teachers, $N$ = teachers who received National honours. "Some teachers are graduates" puts $G$ inside $U$ but not filling it; "only graduates received honours" puts $N$ inside $G$ . So a teacher in $N$ must be in $G$ (II is valid), but a teacher in $G$ need not be in $N$ (I and III are not valid).
(b)
The $n$ th term of a sequence is $2^{2n + 1}$ . Find the first 3 terms of the sequence.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Let the universal set be the teachers in the school, $G$ the graduate teachers and $H$ the teachers who received National honours. "Some teachers are graduates": draw $G$ inside the rectangle, leaving room outside it. "Only graduate teachers received National honours": draw $H$ inside $G$ .

(I)** Mr.
Sowah could be in $G$ but outside $H$ : a graduate with no honour.
So "graduate $\Rightarrow$ honours" is not valid.
(II) $H$ lies wholly inside $G$ , so anyone in $H$ is in $G$ . "Honours $\Rightarrow$ graduate" is valid.
(III) A teacher outside $H$ can still be inside $G$ .
So "no honour $\Rightarrow$ not a graduate" is not valid.

Put $n = 1, 2, 3$ into $2^{2n + 1}$ : $T_1 = 2^3 = 8$ , $T_2 = 2^5 = 32$ and $T_3 = 2^7 = 128$ .