In a certain class, 22 pupils take one or more of chemistry, Economics and Government.12 take Economics (E),8 take Government (G) and 7take Chemistry (C). Nobody takes Economics and chemistry and 4 pupils take Economics and Government.

Question

I) a) using set notation and the letters indicated above, write down the two statements in the last sentence
b) draw a Venn diagram to illustrate the information.
II) how many pupils take
a) both chemistry and government?
b) government only?

Answer 1

I) a) E ∩ C = ∅
b) E ∩ G = 4

II)
a) Let x be the number of pupils taking both chemistry and government. Then from the Venn diagram, we can set up the equation:
x + 4 + (8 - x) + (7 - x) + (12 - 4 - x) = 22
Simplifying and solving for x, we get:
x = 1
Therefore, only 1 pupil takes both chemistry and government.

b) From the Venn diagram, we can see that the number of pupils taking government only is the number in the G circle that is not shared with any other circle. This is (8 - x) = 7, since we found that x = 1 in part a). Therefore, 7 pupils take government only.