Question 1206848: 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) Draw a Venn diagram to illustrate the information.
b) How many pupils take
i) both chemistry and government?
ii) government only?
Answer by ikleyn(52780)   (Show Source):
You can put this solution on YOUR website! .
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) Draw a Venn diagram to illustrate the information.
b) How many pupils take
i) both chemistry and government?
ii) government only?
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We are given a Universal set (22 pupils) and 3 its basic subsets
E (12)
G (8)
C (7)
We also are given their in-pair intersections
EC (0, nobody)
EG (4)
Let x be the number of pupils in the intersection CG.
We know that the triple intersection EGC is 0 (since EC is 0).
Write the inclusion-exclusion equality
22 = 12 + 8 + 7 - 0 - 4 - x + 0,
or
22 = 23 - x.
Hence, x = 23 - 22 = 1.
So, the intersection CG is 1 pupil. It is the answer to question (i).
Government only is G - EG - CG + EGC = 8 - 4 - 1 + 0 = 3. It is the answer to question (ii).
Solved.
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