# Reflexive and symmetric

• Mar 11th 2009, 10:30 PM
jzellt
Reflexive and symmetric
I was asked to show that the divisibility relation is reflexive, but NOT symmetric.

Here is what I did...Let me know if it seems acceptable.

Reflexive:
Assume a|a, for all a e Z. This implies that a = ac, for some c e Z. Abviously if c = 1, this is true. Thus, it is reflexive.

Symmetric:
Assume if a|b, then b|a. I don't know what to do now...

REMEMBER: Don't get | confused with \. | = Divides and \ = Divided by
• Mar 12th 2009, 05:44 AM
danio
For Symmetric you just need to provide a counter example, such as 6/2 = 3 but 2/6 = 1/3 which is not an integer.
• Mar 12th 2009, 05:56 AM
Plato
Quote:

Originally Posted by jzellt
I was asked to show that the divisibility relation is reflexive, but NOT symmetric.
Reflexive:
Assume a|a, for all a e Z. This implies that a = ac, for some c e Z. Abviously if c = 1, this is true. Thus, it is reflexive.

If your set is Z then the relation is not reflexive.
Zero does not divide zero.