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Prove: [itex]Z[/itex]={3k:k[itex]\in[/itex][itex]Z[/itex]}[itex]\cup[/itex]{3k+1:k[itex]\in[/itex][itex]Z[/itex]}[itex]\cup[/itex]{3k+2:k[itex]\in[/itex][itex]Z[/itex]}

[itex]Z[/itex] in this problem is the set of integers

This is all that's given. I thought maybe I could use induction but we haven't reached that topic in class yet. All we've studies is direct proofs, contradiction, contrapositive and some set/set operations stuff.

I have no idea where to start. Maybe element chasing like proving the Demorgan's Laws?