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.
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?
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.
Name us one other number in the equivalence class determined by 4.
How many equivalence classes do you think there are?