I am attempting to work out a problem from my Discreet Mathematics Textbook and am a little stuck on part of this one question. I was wondering if someone could walk me through (b) and (c) on the below?
The question: Determine whether the relation
R on the set of all real numbers is R-reflexive, S-symmetric, AS-antisymmetric, T-Transitive, and/or I-irreflexive, where $(x,y) \in R$ if and only if:
- (a). $y = \pm x$
- (b). $x-y$ is a rational number.
- (c). $xy \ge 0$
- (d). $x = 1$
For (a) and (d) I grew out the graph and referenced my definitions of the above properties to try and determine which the set qualified under, but for (b) and (c) I'm having a difficult time conceptualizing what is being presented so as to determine which properties match up.
Can someone help me with (b) and (c)?