valid or invalid

Question

how to approach these types of question :-

If you work hard & you are talented then you will became musician.

If you became musician , then you will be happy.

You work hard.

You are not talented .

Therefore I will be happy.

Comments

Yes. It is valid!

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What is the approach you are opting? 

tell me this:-

If you work hard you will pass.

You will pass.

Therefore , you work hard

 

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No this is invalid.

If you work hard you will pass. you worked hard. therefore you will pass the exam. This is valid.

(P-> Q. and P hence Q).

But,

This system: If you work hard you will pass. you will pass. Therefore you worked hard is INVALID.

(P->Q. and Q. so P can be True as well as False. In either case, P->Q will be TRUE. Hence can not comment anything about P).

Answer 1

P: You work hard

Q:You are talented

R:You will become musician

S:You will be happy

1. P ^Q->R

2. R->S

3.P

4,Q'

((P^Q->R) ^ (R->S) ^ P ^ Q')->S' as this in not a tautology it's not valid.

Please correct me if I'm wrong

Comments

((P^Q->R) ^ (R->S) ^ P ^ Q')->S'

how does S' came here?