Answer to Question #181832 in Discrete Mathematics for Angelie Suarez

Question

RULE OF INFERENCE

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

Show solution.

1. If I will read my modules, then I can answer all the activities. If I can

answer all the activities, then I will get high scores. Therefore, if I will

read my modules, then I will get high scores.

2. Rizza is an IT student. Therefore, Rizza is either an IT student or a

programmer.

3. If it is national holiday, then school is closed. It is national holiday.

Therefore, the school is closed.

4. If Ann does not love numbers or if Ann does not love programming.

If Ann loves numbers, then she can be a mathematician. Therefore,

Ann can be a mathematician.

Answer 1

1. Let p represent "I will read my modules"

Let q represent " I can answer all the activities"

Let r represent "I will get high scores"

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

This is Hypothetical Syllogism

2. Let p represent "Rizza is an IT student"

Let q represent "Rizza is a programmer"

$p\\ \therefore p \vee q$

This is Addition

3. Let p represent "It is a national holiday"

Let q represent "School is closed"

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

This is Modus Ponens

4. Let p represent "Ann loves number"

Let q represent "Ann loves programming"

Let r represent "Ann can be a Mathematician"

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

This does not follow any rule of inferences.