Are any one of the below relations reflexive, symmetrical, anti-symmetrical or transitive?
a) $$ X = P (\mathbb{Z}). \textrm{ARB if B} \setminus A \textrm{ has only odd numbers and} A \subset B $$
b) $$ \textrm{X is the set of all functions f} : \mathbb{R->R}.\textrm{ fSg if f-g is an even function} $$
c) $$ \textrm{X is the set of all functions f} : \mathbb{R->Z}.\textrm{ fTg if f(1)|g(1)} $$
I do not understand the questions at all. Not what they mean or what they're asking.
a) What is the relation that the question is asking about? is it X or ARB? How are properties like reflexivity expressed in this scenario since they are only defined for binary relations (and P(Z) is not binary?)?
b) what does fSg mean?
c) does | mean or in this context? what is fTg? Is it the same as ARB?