Function fromal definition The relation $R:= \{(x,y) \mid y= \vert x\vert \} \subseteq \mathbb{Z} \times \mathbb{N}$ is a function,
but the relation $R:=  \{(y,x) \mid y= \vert x\vert \} \subseteq \mathbb{N} \times  \mathbb{Z}$ is not a function...
for me it seems that the second relation has also those two properties 1. total left and 2. right-unique....According to my  book I´m wrong :) maybe a hint would help...thx 

For the second $R$ notice that you have $(1,-1)\in R$, $(1,1)\in R$ which is against "right-unique".
