click the flag, then press the buttons on the bottom each different situation represents a singular logic gate that takes two inputs and converts them into one output here's how to turn on the bulb given any logic gate: OR: if either of the switches turn on, the bulb also turns on AND: the bulb only turns on if both other switches are also on NOR: the bulb only turns on if both other switches are turned off NAND: if either of the switches are off, then the bulb turns on XOR: the bulb will turn on if exactly one switch is on - but if both are on, the bulb turns off XAND: the bulb will turn on if the switches are either both on or both off alternatively, here's the same thing in mathematical format OR: x>0 AND: x=2 NOR: x=0 NAND: x<2 XOR: x=1 XAND: x=sqrt(2x)