a) $X$ is the set of real numbers, $n$ is a natural number $R = \{(x, y) \mid x, y \in X, x^n = y^n\}.$
b) $X$ is the set of people in the world $R = \{ (x, y) \mid x, y \in X, x\text{ and }y\text{ share a parent}\}$
I believe both relations are reflexive, symmetric and transitive, aren't they?
I mean, for a) you can have $x^n = x^n \rightarrow (x,x)$, you can have $(x,y)$ and $(y,x) \rightarrow$ symmetric and you can have transitivity by $\leq.$
And for b) it's pretty much the same. As it doesn't say $x$ mustn't be equal to $y$, then you can have $(x,x)$ which is true. You can also have $(y,x) \rightarrow$ symmetry and you can also get transitivity for "if $(x,y)$ is true and $(y,z)$ is true, then $(x,z)$ is true," right?