use Venn-diagram to find examine the validity of the following arguments :
` S_(1)` : All scholars are absent minded.
`S_(2)` : john is a scholar .
S : John is absent minded.
(ii) ` S_(1)` : All scholars ar absent-minded.
(ii) ` S_(1)` : All scholars are absent- minded.
` S_(2) ` : John is not absent minded.
S: john is not absent minded.

Explanation

Let us define the following sets:
A = Set of all absent -minded persons.
B. Set of all scholars.
(i) We observe that the truth of statement `S_(1)` is represented by placing the set B entirely inside the set A i.e. by taking ` B sub A` as shown in Fig.1. Now, the truth of statment `S_(2)` is represented by placing a dot labelled ' John ' inside the set B as shown in Fig. 1.
Now, `S_(1)` is true ` Rightarrow B sub A`
and ` S_(2)` is true `Rightarrow " John" ne B`.
` S_(1) and S_(2)` are true.

` Rightarrow B sub A and " John " ne B`
` Rightarrow " John ne A`
` Rightarrow` John is absent- mind a scholar
S is true .
Hence, the given argument is a valid argument.
(ii) As discussed above the turth of `S_(1)` is represented by taking .` B sub A`. the truth of `S_(2)` is represented by putting a dot labelled 'john' outside set A as shown in Fig .2.

Now , ` S_(1) " is true " Rightarrow B sub A`
and, ` S_(2) " is true " Rightarrow " john " ne A `
` S_(1) and S_(2)` are true
` Rightarrow B sub A and " John " ne A `
` Rightarrow " John ne B`
` Rightarrow` John is not a scholar.
`Rightarrow` S is true.
Hence, the given arugment is a valid argument .