I have read some of the answers on similar questions but I can't really get my head around this.
So, here are 2 questions I need to answer.
Show using a truth table:
That the inference from:
$ p\rightarrow(q \land r),\neg q$ to $ \neg p$ is valid
And the inference from:
$p\rightarrow(q\lor r),\neg q$ to $\neg p$ is not valid.
Ok so if I'm correct a truth table contains all possible situations (or valuations) of an argument. An inference would be getting a conclusion out of two pieces of information $ p\rightarrow(q \vee r),\neg q$ and $\neg p\rightarrow(q\wedge r),\neg q$ respectively for both questions, and drawing a conclusion based on that.
An argument or inference is valid if the conclusion is true as well as the "two pieces of information" or "premises", correct? This would mean that, a situation or "valuation" (only one out of a possible 8 in the case of my examples) where $ p\rightarrow(q \vee r),\neg q, \neg p$ should be true?
So all I would have to do is make a truth table, where all the true-false values are present for the given formulas, and look for a "line" (aka valuation) in the truth-table that has that property?
Because I feel I'm making things way more complex than they have to be. I was looking into modus tollens, but that only applies to a situation where you have 2 formulas and not 3 (as is the case in both of my questions). However if it is possible to answer these questions with modus tollens, how do I do this? Or could you show me how?
Thanks in advance, Rope.
PS. If you could also tell me if my assumption about the definitions of some of the keywords in this question I stated are corect, that would be awesome :P.