Hey folks,
Do anyone of you still remember the problems related to equivalence relations?
Can anyone tell me if the following relations are equivalence relations on the set of integers(z)?
1. "x is related to y" if n only if x=-y
2."x is related to y" if n only if x=3y
3. "x is related to y" if n only if x divides y.
4. "x is related to y" if n only if xy>=0
5. "x is related to y" if n only if x-y is a multiple of 6.

My guess is that 1,2,3,5 are equivalence relations but I remember nothing about it now... Any inputs welcome...

hi bibas, only 3,4 and 5 are equivalence relations. I will tell you why later, may be in 1 or 2 hrs. I have to go now.

hi again
Recall a relation ~ is an equivalence relation if:
a. x ~x i .e. x is related to x
b. x~y implies y~x
c. x~y nad y~z implies x~z
NOw if you look at 1, the condition (a) fails since x is not equal to -x. For 2, again (a) fails since xis not equal to 3x. You can check yourself that for 3, 4 and 5 all three conditions hold.
have fun with math.