1. ## Antisymetric and symmetric

Can some1 explain to me what these means and how i can tell if a relation is symmetric or anti or both?

Im reading the definition over and over for like 10x already and i jsut don't understand.

The example they gave in the book is...

set A {1 2 3 4 }

R = { (2,1), (3,1), (3,2), (4,1), (4,2), (4,3) } is antisymmetric...But why??

What is (a,b) and (b,a) and a=b? i dont understand?

2. Originally Posted by smoothi963

R = { (2,1), (3,1), (3,2), (4,1), (4,2), (4,3) } is antisymmetric...But why??

What is (a,b) and (b,a) and a=b? i dont understand?
Meaning,
If $(x,y)$ and $(y,x)$ then $x=y$.

This is the anti-symettrical property. Check it and convice your self it is true.

Ah! But your problem is that there are no anti-symettrical pairs, for example given $(2,1)$ there is no $(1,2)$. So what! Is it false? No!

This is a strange situation when a statement is true, note, it is never violated.

In symbolic logic,

$(x,y) \wedge (y,x) \to x=y$

This is a conditional statement. Meaning If .... then .... When is a conditional false? When a true statement implies a false statement. Since the initial statement (hypothesis) is always false it means it is always a false implying some statement. That statement is therefore true.