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ktri

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(1) Is R reﬂexive? (If yes, prove it; if no, give a counterexample)

(2) Is R symmetric? (If yes, prove it; if no, give a counterexample)

(3) Is R antisymmetric? (If yes, prove it; if no, give a counterexample)

(4) Is R transitive? (If yes, prove it; if no, give a counterexample)

(5) Is R an equivalence relation?

(6) Is R a partial ordering?

My main issue is I'm not sure how to check if R is symetric or transitive etc. I know what those words mean:

symetric example: \(\displaystyle 4 * 5 = 5 * 4\)

transitive example: \(\displaystyle 2 < 3\) and \(\displaystyle 3 < 4\) so \(\displaystyle 2 < 4\)

but I'm not sure how to determine if R is any of those traits. Like to test if R is reflexive am I checking if

\(\displaystyle |a - b| < 3\) and \(\displaystyle 3 < |a - b|\) ? That dosen't seem right to me. I'm really just not sure what I'm comparing to what.