Answer to Question #343942 in Discrete Mathematics for Abby

Question

Use the rule of inference to obtain conclusion from the each of the set of premises

“If I play hockey, then I am sore the next day.”

“I use the whirlpool if I am sore.”

“I did not use the whirlpool.”

Answer 1

Let

p: I play hockey. q: I am sore the next day. r: I use the whirlpool

1) $p\to q$ premise

2) $q\to r$ premise

3) $\lnot r$ premise

4) $\neg q$ 2 and 3 modus tollens

5) $\neg p$ 1 and 4 modus tollens

Hence the conclusions are "I am not sore the next day", and "I did not play hockey"