# Numerical

• Sep 7th 2009, 04:05 AM
dismath
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.
• Sep 7th 2009, 06:26 AM
Plato
Quote:

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?
• Sep 7th 2009, 06:37 AM
Defunkt
Quote:

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)\$
• Sep 7th 2009, 10:02 AM
dismath
ok, where does z come in? The question doesn't have z. Nothing besides the question is given.
• Sep 7th 2009, 10:31 AM
Plato
Quote:

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?