NECO 2023 · Paper 2 · Q1

Let $U = \{e, f, g, h, i\}$ be a universal set, and $X = \{e, g\}$ and $Y = \{g, h\}$ subsets of $U$ .

(a)
Draw a Venn diagram to represent the information.
Model answer
Draw a rectangle for $U$ and two overlapping circles for $X$ and $Y$ . $g$ is in both sets, so it goes in the overlap. $e$ is in $X$ only and $h$ in $Y$ only. $f$ and $i$ are in neither, so they go inside the rectangle but outside both circles.
(b)
Use the Venn diagram to find (i) $X'$ ; (ii) $(X \cup Y)'$ ; (iii) $X' \cap Y'$ .
Show the answer
(i) $\{f, h, i\}$ ; (ii) $\{f, i\}$ ; (iii) $\{f, i\}$

Worked solution (try it first)

Draw two overlapping circles $X$ and $Y$ inside $U$ : $g$ in the overlap, $e$ in $X$ only, $h$ in $Y$ only, and $f$ and $i$ outside both.

$Y' = \{e, f, i\}$ , so $X' \cap Y' = \{f, i\}$ : the same as (ii), as De Morgan's law says.