I have 3 input variables and the output for all 8 possible combinations is 0 (false). When making a circuit, how would I show this using gates or no gates at all? Thanks!
First you can write down the truth table of your circuit, in this case it will be entirely composed of $0$s. Then you will build up a Boolean expression in the form you prefer (if you have no limitations) which reproduces the behavior (relation input/output) observed in the truth table.
Note that every operator of your boolean expression correspond to a logic gate:
$\land$ = AND
$\lor$ = OR
$\neg$ = NOT
$\oplus$ = XOR