Let $X$ be the set $\{1,2,3,4\}$ and also that $$R = \{(1,1),(1,2),(1,3),(1,4),(2,2),(2,3),(2,4),(3,3),(3,4),(4,4)\}$$
How do I how that $R$ is an equivalence relation; and also its equivalence classes?
I got equivalence class $\{1,2\}$, $\{3,4\}$ but I'm not sure if it's right.
Help appreciated!
Caution: the originally posted relation is not an equivalence relation.
Can you show that symmetry fails? For example: $(1, 3) \in R$, but $(3, 1) \notin R$
For your second problem, can you show that it satisfies reflexivity, symmetry, and transitivity?