Describe the partitions of the equivalence relations for the map $f:(x,y) \mapsto x$.

Question

Question: Describe the partitions of the equivalence relations for the map:

$$f:(x,y) \mapsto x$$

I had a different question on my homework, but I'm not really sure what the question is asking, so maybe if I see the solution for this one example it would clarify things.

Answer 1

This is a projection onto the x-axis, so the relation would be $(x_1,y_1) \sim (x_2,y_2) \iff x_1=x_2$. In other words, the plane is partitioned into vertical lines.