So, I am new to this relations. I have tried to attempt this question by supposing for values but that would not get me anywhere in a formal proof. The question is as follows:
Q. Let a, b ∈ Z, where Z is the set of integers. Define a relation S on Z as aSb
a) iff an + bn is even for some number n
b) iff a^n + b^n is even for some number n
Prove that S is an equivalence relation.
So, I need to prove both of these statements and I am not sure how can I check the properties with it?
To prove a relation we need to check the properties of reflexive, symmetric, and transitive. How can we prove the properties of variables?
NOTE: a and b are 2 different parts. The question is the same though.