Describe the partition of Z resulting from the equivalence relation = (mod 4). Solution a=b mod 4 implies and b give the same remainder modulo 4 There are only 4 least residues modulo 4: 0,1,2,3 So total 4 equivalence classes The partitions are [0]= Multiples of 4 [1]=INtegers of the form 4k+1 [2]=Integers of the form 4k+2 [3]=Integers of the form 4k+3.