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p→ (q→r)

q→ (p→r)

∴(p∨q) →r

how do i prove the validity of this argument by using the rules of inference? please help i'm stuck there is too much possibility that i'm at a lost on how to start...

Ryan gomez
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  • How about using truth tables! – Sujit Bhattacharyya Apr 09 '19 at 14:45
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    You cannot prove it because it is not valid. – Mauro ALLEGRANZA Apr 09 '19 at 14:45
  • why is it not valid? is it because of the number of possible outcomes? – Ryan gomez Apr 09 '19 at 15:29
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    Consider a truth assignment $v$ such that $v(p)= \text T$ and $v(q)=v(r)= \text F$. – Mauro ALLEGRANZA Apr 09 '19 at 18:25
  • i m sorry , i still don't understand, can you explain in more simple terms....i believe that you need to prove that r is false and either p or q is true for the argument to be invalid – Ryan gomez Apr 09 '19 at 23:23
  • ok i did the.truth table for each propositions, i got a situation where p1 was true, p2 was true and conclusion was true..... but i also got the combination where p1 was true, p2 was true but conclusion is false.... im confused... in the book example for modus tonens, when p -> q is true, p is true, you could see clearly that q is true from the truth table and there were no conflicting answers – Ryan gomez Apr 09 '19 at 23:45
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    @Ryangomez As soon as there are 1 or more rows in the truth table where the premises are true and the conclusion is false, then the argument is invalid. The fact that there are other rows where the premises are true and the conclusion is true as well does not take away from this, because a single row with true premises and a false conclusion shows that it is possible for the conclusion to be false while the premises are true, and in order for the argument to be valid, this must be impossible. That is, for a valid argument, the conclusion must always be true whenever the premises are true – Bram28 Apr 10 '19 at 00:21
  • ohhh that makes sense, thanks – Ryan gomez Apr 10 '19 at 00:50

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