I have a question that is focussed on a more language oriented side of propositional logic. In such a way that I have no clue what the question means.
I want to know what the "-q to -p" part means. Is it a iff relation? I have no idea.
Show using a truth table that: the inference from p -> (q & r), -q to -p is valid and the inference from p -> (q | r), -q to -p is not valid
P.S. I couldn't get LaTeX to show me the right signs so I left it like this.
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$\begingroup$There is no "-q to -p" part, if you mean that's supposed to be a unit of the inference up for assessment. It doesn't chunk up like that!
What you are being asked about is, firstly, the validity of the inference from
$$p \to (q \land r), \neg q$$
[those are the premisses] to [the conclusion]
$$\neg p$$
The second case is similar. There are two premisses of which the second happens to be $\neg q$ again, and the conclusion is $\neg p$ again. You are being asked about the validity of that whole inference from the two premisses to the conclusion.
$\endgroup$ $\begingroup$As far as I can see, the first question concerns the inference from a certain set of hypotheses to the conclusion -p. The set of hypotheses consists of the two formulas p --> (q & r) and -q.
$\endgroup$ 3 $\begingroup$$-p$ $-q$ means negation, that is, if it is false then its negation will be true. Negation is just like opposite. That is if it is true then its negation will be false, and if it is false then its negation will be true.
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