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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

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