Verification of Statement: "If Carlo won the competition, then either Mario came 2nd

[zuby]

Verification of Statement: "If Carlo won the competition, then either Mario came 2nd

How do I verify the below sentence?

Formalize the following arguments and verify whether they are correct:

“If Carlo won the competition, then either Mario came second or Sergiocame third. Sergio didn’t come third. Thus, if Mario didn’t come second,then Carlo didn’t win the competition."

I formalized the sentence like:

C -> M v S
~S
~M -> ~C

but how to verify?

 

[pka]

How do I verify the below sentence?
Formalize the following arguments and verify whether they are correct:
“If Carlo won the competition, then either Mario came second or Sergiocame third. Sergio didn’t come third. Thus, if Mario didn’t come second,then Carlo didn’t win the competition."
I formalized the sentence like:
C -> M v S
~S
~M -> ~C
but how to verify?

Here is the argument:
\(\displaystyle 1)\;C \to M \vee S \\ 2)\;\neg S \\ \therefore \quad \neg M \to \neg C \).
Because the conclusion is a conditional, use a conditional proof.

\(\displaystyle 3)~\neg M.~~C.P.\\4)~\neg M\wedge \neg S,~~3\&~2~~conjunction.\\5)~\neg (M\vee S),~~4) negation.\\6)~\neg C, 1)~\&~5) M.T. \\C.P. \neg M\to \neg C.\)

 

[zuby]

Here is the argument:
\(\displaystyle 1)\;C \to M \vee S \\ 2)\;\neg S \\ \therefore \quad \neg M \to \neg C \).
Because the conclusion is a conditional, use a conditional proof.

\(\displaystyle 3)~\neg M.~~C.P.\\4)~\neg M\wedge \neg S,~~3\&~2~~conjunction.\\5)~\neg (M\vee S),~~4) negation.\\6)~\neg C, 1)~\&~5) M.T. \\C.P. \neg M\to \neg C.\)

this is new for me why you used . operator? ~\neg M.~~C.P.

 

[zuby]

Oh I see, thank you very much pka