Let A be the set of all straight lines in the Cartesian plane. Define a relation ∥ on A as follows: For any lines L, M ∈ A, L ∥ M ↔ L is parallel to M. Then ∥ is an equivalence relation on A. Describe the equivalence classes of this relation.

Question

anonymous · Answer

same as all real numbers

anonymous · Answer

$$L\equiv M \iff L, M$$ have the same slope, two lines are in the same equivalence class you can represent them by the real number that is their slope

anonymous · Answer

are you supposed to prove it is an equivalence of just describe the classes?

anonymous · Answer

Just describe the classes. its a discussion question

anonymous · Answer

you don't say the relation is isomorphic, but you could say of you take all line modulo the relation "is parallel" then you get all real numbers

anonymous · Answer

when you look at questions like these, you really want to ask "what do these things have in common?" and that will pretty much give you the equivalence classes

anonymous · Answer

okkkkkkk. Gotcha. Thanks Satellite. That was clear. U R THE BEST :D

anonymous · Answer

being parallel means of course they have the same slope, so everything in the class is represented by the number, whatever the slope is.
yw, (blush)