Turn the rule into gates

The rule we need: turn the light on only when A is 1 and B is 0.

Let's try our gates and see if one already does this.

Start with AND. It only fires when both inputs are 1. So we feed it our winning case, A=1 and B=0. But B is 0, so the two inputs are not both 1. AND outputs 0. The light stays off. Wrong.

Try OR instead. It fires when either input is 1. With A=1 and B=0, it sees a 1, so it outputs 1. Correct, so far. But now flip the inputs: A=0, B=1. OR still sees a 1 and fires, lighting up even though B is the bigger one. Wrong too.

See the problem? AND wants both inputs to be 1. OR is happy with either. But our rule is pickier than both: it wants A to be 1 and B to be 0, specifically. No single gate does that.

Turn the rule into gates

The rule we need: turn the light on only when A is 1 and B is 0.

Let's try our gates and see if one already does this.

Start with AND. It only fires when both inputs are 1. So we feed it our winning case, A=1 and B=0. But B is 0, so the two inputs are not both 1. AND outputs 0. The light stays off. Wrong.

See the problem? AND wants both inputs to be 1. OR is happy with either. But our rule is pickier than both: it wants A to be 1 and B to be 0, specifically. No single gate does that.