Question

Use rules of inference to show that if the premises “All zebras have stripes” and “Mark is a zebra” are true, then the conclusion “Mark has stripes” is true.

Short answer

The conclusion “Mark has stripes” is true for the premises “All zebras have stripes” and “Mark is a zebra” to be true,

Step-by-step solution

Introduction

The rules of inference are a logical structure or guide that develops a conclusion from premises (or hypotheses).

Showing the conclusion is true for the given premises

Following are the premises:

P(x): x is a zebra

Q(x): x has stripes

The statements are:

a) All algebras have stripes

b) Mark is a zebra

c) Mark has stripes

Express these statements in the argument as:

a)\(\forall x\left( {P(x) \to Q(x)} \right)\)

b) \(P(Mark)\)

c) \(\left( {P(Mark) \to Q(Mark)} \right)\)

By modus ponen, the premises (b) and (c) implies\(Q(Mark)\). Since these arguments hold true hence the statement “Mark has stripes” is also true.