Mathematics, 14.09.2019 02:10, guadalupemarlene2001
we define the relation =m (read "equal mod m") on z x z to be the set: {(p, q): m|(p-q)}. show work.
a.) give two pairs which are in the relation =4 and two pairs that are not.
b.) show the =m is an equivalence relation.
Answers: 1
and two pairs that are not.
is equal mod m (written 
) if 
. Then:
is an equivalence relation.
. Then, by definition, 
.Symmetry. It is clear that, given x,y and m such that 
. Therefore 
Transitivity. Let x,y,z and m such that 
and 
. Then, 
. Therefore:![m\mid [(y-x)+(z-y)] \implies m\mid (z-x) \implies x\equiv z \mod m](/tpl/images/0230/6279/2ec55.png)
.
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we define the relation =m (read "equal mod m") on z x z to be the set: {(p, q): m|(p-q)}. show wo...
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