# Thread: Relation given by function

1. ## Relation given by function

I'm having some difficulties on how to show/prove this relation.

Defined function:
⊕:
by

Show that,
~ and ~
then
~

Grateful for any pointers, elaboration!

Bit sorry for the wrong title...

2. your defined function looks fishy to me as its written N^2 x N -> N, although it takes N^2 x N^2 -> N^2 input...

however, the relation to prove is easy as it's just addition of "vectors" or a coupled pair...

3. Sorry, a typo there it should be N^2*N^2->N^2

4. Originally Posted by TiRune
your defined function looks fishy to me as its written N^2 x N -> N, although it takes N^2 x N^2 -> N^2 input...

however, the relation to prove is easy as it's just addition of "vectors" or a coupled pair...
Would you then just show that, since ⊕: $\mathbb{N}^2 * \mathbb{N}^2 \rightarrow \mathbb{N}^2$
And
$(n,m)$ $(k,l)$= $(n+k, m+l)$

That
$(n,m)$ $(k,l)~(n_1,m_1)$ $(k_1,l_1)$

I'm bad at proving these things.... Be gentle...
Which is by defenition

$(n^2*k^2, m^2*l^2)$ which is the same as $(n_1^2*k_1^2, m_1^2*l_1^2)$