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)...
Question 1 Report
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?
Answer Details
(a)(i)
“Nobody takes Economics and Chemistry” is written as
\[n(E\cap C)=0\]
“4 pupils take Economics and Government” is written as
\[n(E\cap G)=4\]
(a)(ii) The Venn diagram is:
(b)(i) Let \(n(C\cap G)=x\). Since \(E\cap C=\varnothing\), there is no triple intersection.
Using the total number of pupils,
\[22=12+8+7-4-x\]
\[22=23-x\]
\[x=1\]
Therefore, the number who take both Chemistry and Government is \(\boxed{1}\).
(b)(ii)
\[\text{Government only}=8-4-1=3\]
Therefore, the number who take Government only is \(\boxed{3}\).
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