- #1

Yankel

- 395

- 0

If R is a partial order relation, is it true to say that

\[R\cup R^{-1}\]

\[R^{2}\]

\[R\cap R^{-1}\]

Are equivalence relations ?

Regarding the first one, I think that the answer is yes. If

\[xRx\]

then it remains after the union. Asymmetry means that \[xRy\] without \[yRx\] but when I apply the union both are in, so it becomes symmetric, and there is no reason why transitive won't work. Am I correct, or not even close ? What about the other two ?

Thank you