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Propositions and truth values.?

if the patient is alive, then the patient is sleeping.
Write the converse, inverse and contrapositive

Statement:
p -> q

Converse:
q -> p

inverse:
~p -> ~q

Contrapositive:
~q -> ~p

So converse:
If the patient is sleeping, then the patient is alive.

Inverse:
If the patient is not alive, then the patient is not sleeping.

Contrapositive:
If the patient is not sleeping, then the patient is not alive.

Here's a good way to remember it:
The word "conversely" when used in normal English tends to flip the sides around: the logic statement follows the same pattern. Inverse just inverts the two variables (not p -> not q). The contrapositive I remember by process of elimination. Or, just have a class that has open-book / open-note tests, so you don't have to memorize pointless shit.

As for the truth values, the statement (implication) and contrapositive always have identical truth values. The converse and inverse always have identical truth values. That actually is sort of important to know, because for a lot of proofs you'll have to switch between implication and contrapositive to get a final conclusion.

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