I need a little help in understand this question:
Let E and F be two sets, R a binary relation on the set E and S a binary relation on the set F. We define a binary relation, denoted RxS, on the set ExF in the following way ("coordinate- wise"):
(a,b) (RxS) (c,d) <--> aRc and bSd.
If R and S are equivalence relations, prove that RxS is an equivalence relation.
The Attempt at a Solution
I said aRc => (a,c) and bSd=> (b,d)
I assumed that aRc and bSd are from ExF.
I'm not sure that what I am doing is right