Answer to Question #182978 in Discrete Mathematics for Maricel

Question

RULE OF INFERENCE:

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

Answer 1

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.