Question

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.

Answer 1

there are 3 properties that satisfy equvalence right?

Answer 2

for any a in A, a ~ a, reflexive

for any a,b in A, a ~ b = b ~ a , symmetric

and then the a~b~c, transitive property

Answer 3

the equivalence classes eh;

like y = mx + b, where m is held constant

Answer 4

in order to define all lines; like the x=k that have undefined slopes ... i wonder if you could throw in an exception that defines it; or if youd have to resort to the Ax+By=C form