We have $A = \{1,2,3,4 \}$ and the relation $R = \{(2,1), (3,1), (3,2), (4,1), (4,2), (4,3) \}$.
My book is saying that this is antisymmetric, but I cannot figure out why. I know the definition is $\forall a \forall b(((a,b)\in R \land (b,a)\in R) \rightarrow (a=b)).$
I used the definition here and I am not getting anywhere. Does someone else have a recommendation on how to look at this problem?
Are there elements $a,b\in A$ such that both $(a,b)$ and $(b,a)$ belong to $R$? No, there aren't. So, the assertion$$(a,b)\in R\wedge(b,a)\in R\implies a=b$$is vacuously true.