E) given the following: let x = {1, 2, 3, 4) and a relation r on x as r= {(1,2), (2,3), (3,4)}. find the reflexive and transitive closure of r.

The answer is

Step-by-step explanation:

Remember that a reflexive relation , where is the power set of , is one which conteins the ordered pairs of the form , for .

So, As the reflexive and transitive closure of (that we will denote by ) is in particular reflexive, we must add to  the elements

A transitive relation is one in which if the pair and the pair are in there, then the pair must be there too.

So, to complete the relation to be reflexive and transitive we must add the pair (because are in ), the pair , and the pair because we added the pair .

Therfore we have that .

a is the correct