In this question ( section 2.2 #2) is asking to determine which of the 3 propert

Question

In this question ( section 2.2 #2) is asking to determine which of the 3 properties are satisfied by the given relation R defined on set S.---------------- S={1,2,3} and R={(1,1),(1,3),(2,2),(2,3),(3,1),(3,2),(3,3)}. ------ The answer Chegg provides is not very clarifying, so please explain as to which properties it does satisfy and a more down to earth explanation to the answer. Thank you in advance!

Explanation / Answer

on the set S = {1,2,3} given relation R is reflexive as x~x for all x in S. since (1,1), (2,2) and (3,3) all belong to R, x is always related to itself for all x in S. Hence given relation is reflexive. for any x~y ie (x,y) in R, we can check by inspection that y~x also ie (y,x) also belongs to R. example, (1,3) is in R. So is(3,1). Hence the given relation is symmetric. Given relation is not transitive. for transitivity we must have x~y and y~z => x~z. But we can see (1,3) is in R, and (3,2) is in R ie 1~3 and 3~2 but 1~2 is not true as (1,2) does not belong to R. Hence given relation is not transitive.

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