I'm having trouble determining which properties work/don't work, as well as how to go about proving them:
Determine whether the given relation R on the set A is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. Justify your answer for each of the six properties.
a. 𝐴 = ℤ+; (𝑎, 𝑏) ∈ 𝑅 if and only if |𝑎 − 𝑏| ≤ 2.
b. 𝐴 = ℤ+; (𝑎, 𝑏) ∈ 𝑅 if and only if gcd(𝑎, 𝑏) = 1.
(if you guys could tell me which properties work/don't work only, that would also be helpful)