Forty students are available for three activities: Art $(A)$, Dancing $(D)$ and Gardening $(G)$. Five students do not join any of the activities. Twelve take Art only. Four take both Dancing and Gardening, but not Art. One student takes part in all three activities.
(a)[2]
Fill in the Venn diagram.
(b)[3]
On the Venn diagram, $x:y:z = 1:2:3$. Determine the value of each of $x$, $y$ and $z$.
(c)[1]
In part (a), one subset of the Venn diagram contains no students. State this subset in set notation.
(d)[1]
Determine $n((D \cup G) \cap A)$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Given numbers placed in the correct regions” …