1. ## Numerical

I desperately need help with this numerical:
Consider the following relation R on A ={1,2,3,4,5,6,7}. The relatin holds for numbers x,y if x-y is a multiple of 3.
Check whether R is reflexive, symmetric, transitive and anti-symmetric.

I need to show the process as well.
Any help will be highly appreciated.
Thanks.

2. Originally Posted by dismath
I desperately need help with this numerical:
Consider the following relation R on A ={1,2,3,4,5,6,7}. The relatin holds for numbers x,y if x-y is a multiple of 3.
Check whether R is reflexive, symmetric, transitive and anti-symmetric.
Is $\displaystyle x-x$ always a multiple of 3?

If $\displaystyle x-y$ is a multiple of 3, then is $\displaystyle y-x$ a a multiple of 3?

If $\displaystyle x-y~\&~y-z$ are a multiples of 3, then is $\displaystyle x-z=(x-y)+(y-z)$ a multiple of 3?

3. Originally Posted by Plato
Is $\displaystyle x-x$ always a multiple of 3?

If $\displaystyle x-y$ is a multiple of 3, then is $\displaystyle y-x$ a a multiple of 3?

If $\displaystyle x-y~\&~y-z$ are a multiples of 3, then is $\displaystyle x-z=(x-y)-(y-z)$ a multiple of 3?
Surely, in the last line you meant $\displaystyle x-z = (x-y)+(y-z)$

4. ok, where does z come in? The question doesn't have z. Nothing besides the question is given.

5. Originally Posted by dismath
ok, where does z come in? The question doesn't have z. Nothing besides the question is given.
What does the transitive property say? Do you know?