Step 1: Test the AND gate.
An AND gate gives 1 only when both inputs are 1. For inputs $(0,1)$ and $(1,0)$, it gives 0 both times.
Step 2: Test the NOR gate.
A NOR gate gives 1 only when both inputs are 0. Since both $(0,1)$ and $(1,0)$ contain a 1, the output is 0 both times.
Step 3: Pick the pair.
Both AND and NOR give 0 for these inputs. \[ \boxed{\text{NOR and AND}} \]