(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.)

(a)

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

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

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

(b)

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