How to show all false outputs in a circuit?
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