There are 650 voters in the voter list of a Trade Union Election. They are allowed to cast vote either only for A or for B as the president of the union. 15 people didn't cast the vote and 12 voters cast vote for both the candidates. The candidate A won the election with the majority of 325 voters.

1. Show these information in a Venn-diagram.
2. How many people of the voter list cast the vote?
3. Find the number of valid votes.

Solution:

Let U be the set of total people who casted their vote in the election.

Let A and B be the sets of votes received by candidates A and B, respectively.

According to the question,

$n(U) = 650$

$n_(A) = n_o(B) + 325$

$n(A \cap B) = 12$

$n(A \cup B)^c = 15$

Total voters from the voters list who cast the vote are:

$= n(U) - n(A \cup B)^c$

$= 650 - 15$

$= 635$

Total valid votes cast in the election are:

$= 635 - n(A \cap B)$

$= 635 - 12$

$= 623$

Note: Make correction in your vedanta Excel in Mathematics book 10 if it has been written 212 voters cast vote for both. Make it 12 voters.

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