SOLUTION: 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 economic

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(52778) (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?
~~~~~~~~~~~~~~~~~~~~~

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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