Question

Use First Order Logic reasoning to prove that the negation of transitive relation is intransitive.

Answer 1

Transitive relations are relations in which if an element a is related to an element b and element b is related to an element c then element a is related to element c.

Intransitive relations are relations in which if an element a is related to an element b and element b is related to an element c then element a is not related to element c.

First, we will find the first order logic statement for transitive relation:

It can also be written as:

Now negate it:

This can only be true when element a is related to element b and element b is related to element c but element a is not related to element c which is intransitive.