Q1 SET THEORY

In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals?

Let the distribution of votes for each of the proposal be as given below.

From the information given, we know that

a+b+c+d+e+f+g = 78-(1)

a+b+e+f=50(2)

b+c+f+g = 30 -- (3)

e+f+g+d=20-(4) and

f=5-(5)

We need to find b+e+g+f=?

In the above equations, (2)+(3)+(4)-(1) implies

(a+b+e+f)+(b+c+f+g)+(e+f+g+d) - (a+b+c+d+e+f+g) = 50+30+20-78 = 22

Or, b+e+g+2f=22.

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