



 
Hi Jim, A relation on a set S is an an equivalence relation if it satisfies three properties
Your first relation is reflexive (x = x) and symmetric (if x = y then y = x) and transitive (if x = y and y = z then x = z) so the relation is an equivalence relation. Now try the second relation. Does it satisfy all three properties? For the third relation use the properties of congruence to show it is an equivalence relation. Harley
 


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