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A relation is antisymmetric if the only way for (b,a) to exist for (a,b) is that a=b.

## Examples

### R is a relation over the set A

• $A={1,2,3}$
• $R={(1,1),(1,2),(2,3)}$

R is asymmetric because there is no (3,2) for (2,3) in R. The only way for (a,b) and (b,a) to coexist is that a=b.

### R is a relation over the set A

• $A={1,2,3}$
• $R={(1,2),(2,3),(3,1)}$

R is asymmetric because there is no (b,a) for (a,b) that a does not equal to b.