Show using rules of inferences whether these arguments are valid or not:

$13\mathrm{.}1$Somebody in this class enjoys whale watching. Every person who enjoys whale watching cares

about ocean pollution. Therefore, there is a person in this class who cares about ocean pollution.$.$

$13\mathrm{.}2-$ Given:

p $->$ r

$($p $$ q$)$

Therefore: $$ r

$13\mathrm{.}3$

$$She is a Math major or a Computer Science major.$$

$$If she does not know Discrete Mathematics, she is not a Math major.$$

$$If she knows Discrete Mathematics, she is smart.$$

$$She is not a Computer Science major.$$

Therefore, $$she is smart.$$

$13\mathrm{.}4$

$$It is not raining and it is not cold.$$

$$If it is not July, then it is rainy or cold.$$

$$If it is July or August, then it is rainy.$$

Therefore: $$It is rainy.$$