Question

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?
) Both Chemistry and Government
i) Government only​

Answer 1

a) i) Using set notation and the letters indicated above, the two statements in the last sentence are:
- E ∩ G = 4 (4 pupils take Economics and Government)
- E ∩ C = ∅ (nobody takes Economics and Chemistry)

ii) Here's a Venn diagram to illustrate the information:

```
C
/ \
/ \
/ \
E-------G
\ /
\ /
∅
```

b) To find out how many pupils take both Chemistry and Government, we need to add up the number of pupils in the intersection of the two sets C and G. From the Venn diagram, we can see that the intersection contains 2 pupils. Therefore, 2 pupils take both Chemistry and Government.

To find out how many pupils take Government only, we need to subtract the number of pupils who take both Government and another subject from the total number of pupils who take Government. From the information given, we know that 8 pupils take Government, and 4 of them also take Economics and Government. Therefore, the number of pupils who take Government only is:

8 - 4 = 4

Therefore, 4 pupils take Government only.