I have, say a gate with 3 inputs C X Y and two outputs Z W , with the following truth table :

C X Y Z W
0 0 0 0 0
0 0 1 0 1
0 1 0 1 0
0 1 1 1 1
1 0 0 0 0
1 0 1 1 0
1 1 0 0 1
1 1 1 1 1

I am challenegd to prove it functionally complete by just showing that this gate can implement AND and NOT gate...I tried to figure out many boolean functions for Z and W but no luck. Some1 please kindly help me.

 

You need to post your attempts at working the problem in order to give us a starting point from which to help you.

Just by inspection, there are several ways to get a NOT gate and two obvious way to get an AND gate, so a solution does exist.

Do you recognize this truth table at all?