Discrete Math:
Need some help to figure out the equivalence relation on N.
Equivalence class {0} =[0,1,2,3,4,5…] when values of m^2 and n^2 are
the same.
Equivalence class {1} does not seem to exist or is an empty set {}.
The only classes that exist are class {0} and class{N}.
Please scroll down to page 2 to see my work trying to prove parts a and
c on this problem. Please check over to see where I went wrong. Thank
you.
Mathematics Homework Solutions
#94088
Equivalence Relations and Classes
For m, n, in N define m~n if m^2 - n^2 is a multiple of 3.
(a.) Show that ~ is an equivalence relation on N.
(b.) List four elements in the equivalence class [0].
c) List four elements in the equivalence class [1].
(d.) Are there any more equivalence classes. Explain your answer.
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