i have a question and i am stuck on the first part was wondering if you could help.
Let R be the set of real numbers. Define a relation R(subscript1) on the set R as follows: m R(subscript1) n whenever n-m congruent to 0(mod24).
First off how do i define this relation?
I then have to proove R(subscript1) is an equivalence relation but i want to give this a bash first once i managed to define the relation.
ordered pairs is what you would know as coordinates, sort of
like (m,n) is an ordered pair.
now, a relation is a set of such pairs. thus, saying is the same as saying , that is, the ordered pair (m,n) is an element of the (set) relation . note that the relation is on the real numbers, this means that m and n are real numbers
the relation has been defined for you, you do not have to do that. simply prove it is an equivalence relation in the way Plato said. you do know the definitions of "reflexive", "symmetric" and "transitive", right?