Sorry for the repeat of questions. I had not realize if I put the other in the r

Question

Sorry for the repeat of questions. I had not realize if I put the other in the right place.
I am working on two problems that seem to be similar. The first question is: Suppose R is a relation on a set A, then R is transitive iff R o R is a subset of R. The "o" here means composition.

The other question which I feel is very similar and can be solved with the help of the first one is :

Suppose that R is a relation on a set A which is transitive and reflexive. Then R o R=R. Again, "o" here is composition.

I really don't understand how the transitive/reflexive portions connect with the composition here. I also don't understand how R composition with itself (R) works

Explanation / Answer

In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c. In mathematical syntax: , but also shorter . Transitivity is a key property of both partial order relations and equivalence relations.

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