$R = \{(f,g) \mid f(0) = g(0)\;\text{or}\; f(1) = g(1)\}$ The relation is... Let $A$ be the set of all functions from the set of integers to the set of integers, and let $R$ be the relation on $A$ given by
$$
R = \{(f,g) \mid f(0) = g(0) \;\;\text{or}\;\;f(1) = g(1)\}
$$
The relation is:
(a) reflexive, symmetric, anti-symmetric, not transitive.
(b) reflexive, symmetric, not anti-symmetric, and not transitive.
(c) not reflexive, not symmetric, anti-symmetric, and not transitive.
(d) reflexive, symmetric, not anti-symmetric, and transitive.
I'm not really sure how to go about this problem. I know how I can use the elements in the logical defintions of symmetric relations, but I'm not sure what elements I'm putting in.

To be reflexive means that for all functions $f\in A$, holds that $fRf$. Now, is it the case that $fRf$? Let's see, it would hold if $f(0)=f(0)$ or $f(1)=f(1)$. Well, certainly then $fRf$. Now you can work through the other properties and check them for this relation. 
