1) Recall that an equivalence relation S on set R ( R being the reals) is a subset of R x R such that(adsbygoogle = window.adsbygoogle || []).push({});

(a) For every x belonging to R (x,x) belongs to S

(b) If (x,y) belongs to S, then (y,x) belongs to S

(c) If (x,y) belongs to S and (y,z) belongs to S then (x,z) belongs to S

What is the smallest equivalence relation S on the Set R of real numbers that contains all the points in the line y - x = 1. Prove your answer.

Can anyone help figure this out? I am pretty lost on this one.

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# Homework Help: Equivalence Relations

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