Define a relation ~ on N by a~b iff a=b*5^k for some k that is a member of Z.

a) Prove that ~ is an equivalence relation on set N

b)Give a complete set of equivalence class representatives.

(Angry)

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- September 16th 2008, 02:02 PMmandy123Prove
Define a relation ~ on N by a~b iff a=b*5^k for some k that is a member of Z.

a) Prove that ~ is an equivalence relation on set N

b)Give a complete set of equivalence class representatives.

(Angry) - September 16th 2008, 02:37 PMPlato
- September 16th 2008, 02:57 PMmandy123
ok so how in the world did you figure out the first part?? I am so confused with how you went from the variables a,b,k to the variables c and j?

The second part (b) will those be the equivalence class representatives.

I know that 4,23,65 are not the same equiv. classes, but 5, 50, 75 are the same equiv classes. Right? - September 16th 2008, 03:33 PMPlato
Do you know what equivalence relation is?

If you do, then you recognize that as a proof that the relation is an equivalence relation.

By the way, a, b & c are natural numbers. While k & j are of course integers.

Do you really know that?

Name us one other number in the equivalence class determined by 4.

How many equivalence classes do you think there are?