**A sample poll of 135 voters revealed the following information in favour of three A ,B and C of a certain political party in Abia state. 60 were in favour of B; 23 were in favour of A alone; 17 were in favour of C alone; 10 were sitting on the fence; 55 were in favour of exactly two candidates; 61 were in favour of exactly one candidate; 46 were in favour of candidate A and at least one other candidate. How many people were in favour of (a) both B and C (b) A and B only? (c) A or C**

The **Answer to the Question**

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**Here's the Solution to this Question**

$|S|=135, |A\cup B \cup C|=135-10=125$

$|A\ alone|=23, |C\ alone|=17,$

$|B\ alone|=61-23-17=21$

$y+z+w+21=60$

$x+y+z=55$

$x+y+w=46$

$61+55+w=125$

Then

$w=9$

$x+y=37$

$y+z=30$

$z=18$

$x=25,y=12,z=18,w=9$

(a)

$|B\cap C|=18+9=27$

(b) A and B only?

$|A\ and\ B\ only|=12$

(c)

$|A\cup C|=23+17+25+9=74$