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.

Step-by-step explanation:

a) Give two pairs which are in the relation and two pairs that are not.

As stated before, a pair is equal mod m (written ) if . Then:

b) Show the is an equivalence relation.

An equivalence relation is a binary relation that is reflexive, symmetric and  transitive.

By definition is a binary relation. Observe that:

.

In conclusion, defines an equivalence relation.

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

step-by-step explanation:

the line of