In a certain class, 22 pupils take one or more of Chemistry, Economics and Government. 12 take Economics (E), 8 take Government (G) and 7 take Chemistry (C). Nobody takes Economics and Chemistry and 4 pupils take Economics and Government.
(a)(i) Using set notation and the letters indicated above, write down the two statements in the last sentence; (ii) Draw a Venn diagram to illustrate the information.
(b) How many pupils take (i) both Chemistry and Government ? (ii) Government only?
Explanation
(a)
(i) Nobody takes Economics and Chemistry (n(E cap C) = null ).
(ii) 4 pupils take Economics and Government; (n(E cap G) = 4)
(b) (i) Suppose (n(C cap G) = x)
(22 = 8 + 4 + 8 – 4 – x + x + 7 – x)
(22 = 23 – x implies x = 1)
Only 1 person does Chemistry and Government.
(ii) Number taking only Government = (8 – (4 + x))
(8 – (4 + 1) = 3)