Hello, noob on here. Having trouble proving an equivalence relation...
Given:
Define a relation R on
(the integers) by
if
is a multiple of 5.
a. Show that R is an equivalence Relation
b. How many equivalence classes are there for R?
a. I know that in order to prove an equivalence relation, you must show that a relation is reflexive, symmetric and transitive.
Reflexive, nRn
Let x be an element of n
0 is a multiple of 5
therefore, nRn
therefore, R is reflexive.
I have no idea how to go about proving Symmetric and Transitive without using actual numerical values.
b. I do not know how to determine the number of equivalence classes exist for R.
Thanks in advance, sorry I don't have more to offer.
Gavin