Theory question 103
SetsIn 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?
Show the model answer
(a)(i) E ∩ C = ∅ (or n(E ∩ C) = 0); n(E ∩ G) = 4
(ii) Circles E and G overlap (4 in the overlap); circle C overlaps G only and does not touch E; let x be in C ∩ G
E only = 8, G only = 4 − x, C only = 7 − x
(b)(i) 8 + 4 + (4 − x) + x + (7 − x) = 22, so 23 − x = 22 and x = 1
(ii) Government only = 8 − 4 − 1 = 3
Draw the C circle so that it does not overlap E, because nobody takes both.