USING THE RULES OF INFERENCE:

?? ? ?? ? ?? } Addition / ?? ? ?? ? ?? } Simplification / ?? ?? ? ?? ? ?? } Conjunction / ?? ? ?? ?? ? ?? ? ?? ? ?? } Resolution / ?? ?? ? ?? ? ?? } Modus Ponens / ?? ?? ? ?? ? ?? } Modus Tollens / ?? ?? ? ?? ? ?? } Disjunctive Syllogism / ?? ? ?? ?? ? ?? ? ?? ? ?? } Hypothetical Syllogism

1. Determine whether or not the following arguments are valid. If they are valid, then state the rules of inference used to prove validity. If they are invalid, outline precisely why they are invalid.

a. If it is summer, then it is humid outside. If Santa is delivering presents, then it is not the case that it is hot and humid outside. It is currently hot outside and Santa is delivering presents. Therefore, it must not be summer.

b. If it is Thursday, then I do not have to go to class. I do not go to class. Therefore, it must be Thursday.

c. Everyone taking COMP1805 loves math. Everyone taking STAT 2507 loves math. Therefore, everyone in STAT 2507 is taking COMP 1805.