Determine if the following argument is valid. Explain by using rule of inference. (5 pts each) 1. If you perform every programming problem in the module, then you will learn programming. You learned programming. Therefore, you perform every programming problem in the module. 2. Not everyone likes to go to the hospital; hence, there is someone who does not like to go to the hospital

1. Let p represents you perform every programming problem in the module.

Let q represents you will learn programing

We have

$p\to q\\ q\\ \therefore p$

This is invalid. Assume that $p\to q$ and q are both true. Now, $p\to q$ may be true with p being false. Then the conclusion p is false is invalid. Hence the argument is not valid by fallacy of Converse.

2. Let p represents everyone likes to go to the hospital.

Let q represent that there is someone that likes to go to the hospital.

We have

$\neg p\\ \therefore \neg q$

If the premises is true then the conclusion will also be true. Hence the argument is valid.