I just started working with functions in my discrete mathematics class and we got presented with these two problems to think about at home. If anybody could help me out with them and explain, I'd greatly appreciate it.
Problem 1
Let $R$ be a relation on a set $A$. Then $R$ is transitive iff $R\circ R$ is a subset of $R$.
Problem 2
Suppose that $R$ is a relation on a set $A$ which is reflexive and transitive.
Then $R\circ R = R$.