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)   (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"
-------------------------------------------------------
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)
|
|
|
