draw conclusion (logic)

Question

What is the correct approach for drawing a conclusion from

P1:- If it rains ,the match will not be played .

P2:- The match was played

A) it rains

B) it did not rain

C) it either rain or did not rain

D) None

Answer 1

It's option B It did not rain.

P- It rains

Q-Match was not played

By Modus Tollen Q'^(P->Q) -> P'

Comments

do you have anything to say about your in question that i asked 

valid or invalid

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I also had doubt regarding that while solving I think it's English Jargon but logically it means You're not happy as we can solve the validity considering negation of You are happy.

Logically also to make conclusion we cannot take new variable as used in premises. See rule of inferences for more clarity as they are building block of complex valid invalid arguments

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I just asked that from where you get S'  in that expression