Question

(d) Prove the validity of following arguments :
If man is a bachelor, he is unhappy
If a man is unhappy, he dies young
Therefore, bachelors die young
[Example 3. Page 185 of Spectrum A​

Answer 1

Step-by-step explanation:

man is a bachelor, he is unhappy

If a man is unhappy, he dies young

Therefore, bachelors die young

Answer 2

Question :

Prove the validity of following arguments :

If man is a bachelor, he is unhappy.

If a man is unhappy, he dies young.

Therefore, bachelors die young.

Answer :

The given statement is valid.

Let us first consider the sets :

A = Set of all unhappy men.

B= Set of all bachelors.

C = Set of all men who die young.

Then, the truth of the hypothesis S1 is represented by placing the B inside the set A ,

B ⊆ A

The truth of the statement S2 is represented by placing the set A inside the set C completely,

A ⊆ C

Therefore the hypotheses S1 and S2 are true where

B ⊆ A and A ⊆ C

Hence, B ⊆ C

Therefore, All bachelors die young.

The statement S is true.

Hence, the given arrangement is a valid argument.

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