Use venn-diagram to check the validity of the following argument :
`S_(1)` : if a man is a bachelor, he is unhappy.
`S_(2)`: If a man is unhappy , he dies young .
S : All bachelors die young.

Answer

given statement is valid

Explanation

Let us first define the following sets:
A = Set of all unhapply man.
B= Set of all bachelors, ,
and , C = Set of all men who die young. Then, the truth of the hypothesis `S_(1)` is represented by placing the B inside the set A i.e. by ` B sub A`. Now, the truth of statement `S_(2)` is represented by placing the set A completely inside the set C i.e. by `A sub C`.

Now,
`S_(1) and S_(2) ` are true.
` Rightarrow B sub A and A sub C`
` Rightarrow B sub C`
`Rightarrow` All bachelors die young
`Rightarrow ` S is true.
Hence, the given arrugment is a valid argument.