For each of the following relations on the set of all integers, determine whether the relation is reflexive, symmetric, and/or transitive:
a. (𝑥,𝑦)∈𝑅 if and only if 𝑥<𝑦.
b. (𝑥,𝑦)∈𝑆 if and only 𝑥𝑦≥1.
c. (𝑥,𝑦)∈𝑇 if and only 𝑥=−𝑦.
d. (𝑥,𝑦)∈𝑈 if and only 𝑥=|𝑦|
I've made some attempts at solving these of course, but have only yielded fitting answers for b and d, which I know are symmetric/transitive, and solely symmetric, respectively (unless I made some errors in deducing this which is definitely not out of the question). I even tried looking at post like the one below to determine whether or not what I was doing was correct, but it didn't provide much I could really use.
I appreciate your help and assistance