   Chapter 6.4, Problem 22ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# (a) Assuming that the following senetec is a statement, provce that 1+1=3; If this sentence is true, then 1+1=3, (b) What can youdeduce from part (a) about tha status of “This sentence is true”? Why? (This example is known as Lob’s parabox.)

To determine

(a)

Assuming that the following sentence is a statement, prove tha 1+1=3 :

If this sentence is true. then 1+1=3.

Explanation

Given information:

Each sentence is a statement.

Concept used:

In general, in the implication, A B(if A then B), A stands for the antecedent, and, B stands for the consequent.

Calculation:

Consider that the following sentence is a statement

“If this sentence is true, then 1+1=3 ”.

In general, in the implication, A B(if A then B), A stands for the antecedent and B stands for the consequent

Here, the antecedent, A is this sentence is true, and the consequent, B is 1+1=3.

Suppose the antecedent is true, and consequent is false

Then, the sentence “If this sentence is true, then 1+1=3 ” is true, because the truth value of the antecedent. -this sentence is true is true.

In general the “If then” sentence is false, only when the antecedent is true, and consequent is false.

The truth table for “If then” is shown below

To determine

(b)

What can you deduce from part (a) about the status of “This sentece is true”? (This exaple is known as Lob’s paradox).

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