SOLUTION: Define a relation R on the set of integers by mRn if and only if 3 divides m - n. Prove or disprove that R is reflexive. This is what I have, the problem is i'm not sure where I

Algebra ->  Proofs -> SOLUTION: Define a relation R on the set of integers by mRn if and only if 3 divides m - n. Prove or disprove that R is reflexive. This is what I have, the problem is i'm not sure where I      Log On


   

Question 742285: Define a relation R on the set of integers by mRn if and only if 3 divides m - n.
Prove or disprove that R is reflexive.
This is what I have, the problem is i'm not sure where Im supposed to get to.
Assume mRn and let 3 divide m-n, for some integers m and n.
By definition of divides, 3=(m-n)(k), for some integer k.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You have the definition of divides mixed up, it should be this

if 3 divides m - n

then 3k = m-n

basically "if 3 divides x, then 3 is a factor of x"

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To prove it is reflexive, you need to show that mRm is true for any integer m

This is quite simple since 3k = m-m leads to 3k = 0 which implies that k = 0

So for any number m, mRm is true. In other words, any number m is related (in terms of R) to itself since 3 divides m-m or since 3 divides 0 (3 is a factor of 0)