# Math Help - set and relation

1. ## set and relation

about the relation R={ (n,m)∈ N×N: ∃r ∈ N: n^2 + m^2 = r^2}
N is set of natural number.

a)how to show the converse of R is equal to R?
b)how to prove R is not the empty relation?
c)how to prove R is not a function?

2. Originally Posted by nyammo
about the relation R={ (n,m)∈ N×N: ∃r ∈ N: n^2 + m^2 = r^2}
a)how to show the converse of R is equal to R?
b)how to prove R is not the empty relation?
c)how to prove R is not a function?
a) You must mean inverse as in $R=R^{-1}$.
Note that if $m^2+n^2=r^2$ then $n^2+m^2=r^2.$

b) Is it true that $(3,4)\in R~?$

c) Is every term of $N$ the first term of some pair in $R~?$