Answer to Question #180886 in Discrete Mathematics for Angelie Suarez

Question

E. What rule of inference is used in each of the following arguments? Show

solution. (5 pts each)

1. If it will rain today, then the classes are suspended. The classes are not

suspended today. Therefore, it did not rain today.

2. If you read your module today, then you will not play ML today. If you

cannot play ML today, you can play ML tomorrow. Therefore, you read

your module today, then you will play ML tomorrow. 

Answer 1

1. Let p represent it will rain today

Let q represent the classes are suspended.

So we have

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

This is Modus Tollens

2. Let p represent You read your module

Let q represent You will play ML today

Let r represent You will play ML tomorrow

$p\to \neg q\\ \neg q \to r\\ \therefore p \to r$

This is Hypothetical Syllogism