
equivalence relation
Which of the following relations is an equivalence relation?
(a) {(1, 1), (2, 2), (3, 3), (1, 2)}
(b) {(a, b)  (a = b) v (a is odd ^ b is even)}
(c) {(x, y)  x + y is even}
(d) {(t1, t2)  t1 and t2 are triangles, and some angle in t1 is equal to some angle in t2}
I know the answer is (c), but my question is how do you even work on (a) when it's just a list of points?

I guess that by (1,1) they mean 1 related to 1, (2,2) 2 related to 2, etc.
As for c) as I understand it you have x related to y if x+y is even.
Of course x is related to himself because 2x is even.
If x is related to y then y is related to x because of the commutativity of addition (I guess you work in N Z Q or R).
If x is related to y and y related to z then x is not necessarily related to z. Think of the case where you have three odd numbers.
Maybe I made a stupid mistake but does that make sense to you?
As for d, a triangle is related to itself because it has the same angles.
The relation is also symmetric but not transitive.
It may be b) but I don't really understand your notation.