SOLUTION: For each of the following, write the set in an appropriate notation. The set of numbers that have a remainder of one when you divide by four.

They are all 1 more than a multiple of 4.  
In roster notation they are:

{1,5,9,13,17,...}

  0      1      2        3        4 
4)1    4)5    4)9     4)13     4)17
  0      4      8       12       16
  1      1      1        1        1

So you see, when we divide by 4, the remainder is always 1.

So we take 4k, where k is a whole number, and then add 1
to it.

So the set is the numbers n of the form 4k+1, where k
is any whole number:

The set-builder notation is

{n | n=4k+1, k is a whole number}

The whole numbers are 0,1,2,3,4,...

Edwin