I have been asked to determine whether the following is a tautology or not:
$((p \wedge q) \wedge \sim P)) \rightarrow P $
I am confused whether the uppercase 'P' is just a misprint or it actually means something in this context. Almost 20% of the questions in the question set use uppercase letters while the majority doesn't. I do not have the answer set available to myself right now and googling this was not much help either.
Please clarify this for me.
Lowercase letters are typically used for propositional variables, i.e. symbols representing atomic statements, which always have the concrete truth table given, whereas uppercase letters may be used for formula schemata, i.e. placeholders for arbitrarily complex formulas, which may have special properties in their truh value distribution. For instance, while $P \lor Q$ is in the general case a contingent statement, it may have tautological instances, such as $P = p$ and $Q = \sim p$, where the rows where neither of $P$ and $Q$ are true can not actually exist for this instance. If that is the meaning of the uppercase symbols, you have to think about whether particular instances make a difference to the tautologicity.