Composition of relations (can't I disprove this?)

[manx182]

I have a problem with this proof question, mainly because I think it is invalid. Let's see what you think. Surely an input of x = 7 , y = 2 would disprove this?

"Let M2 and M3 be relations on Z (set of integers) defined as follows:

" e" - is of the set

(x,y) e M2 if and only if x-y is divisible by 2

and

(x,y) e M3 if and only if x-y is divisible by 3

Prove that the composition of M2 and M3 is the complete relation on Z. (i.e M2 o M3)

 

[pka]

I don’t know the definition of ‘complete relation’.
That is not a standard term used in set theory.

However, \(\displaystyle \L
(7,2) \in M_2 \circ M_3 \mbox{ because } (7,4) \in M_3 \quad \& \quad (4,2) \in M_2 .\)