a diagram of your switch could look like this:
A1 A2
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battery xxxxxxxxxxxxxxx C1 C2 xxxx light xxxxx ground
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B1 B2
you have battery coming in from the left going through the switches and then through the light and then to ground.
the following connections are possible through switch 1 and switch 2.
switch 1 switch 2 light
C1 to A1 C2 to A2 ON
C1 to A1 C2 to B2 OFF
C1 to B1 C2 to B2 ON
C1 to B1 C2 to A2 OFF
if we let:
C1 to A1 = UP
C1 to B1 = DOWN
C2 to A2 = UP
C2 to B2 = DOWN
then the table becomes:
switch 1 switch 2 light
UP UP ON
UP DOWN OFF
DOWN DOWN ON
DOWN UP OFF
this becomes the basis for your truth table.
in order to construct the truth tables, we will have 4 variables.
they will be U1, U2, D1, D2
U1 means switch 1 is up.
U2 means switch 2 is up.
U3 means switch 3 is down.
U4 means switch 4 is down.
T means True means the switch is as indicated.
F means False means the switch is not as indicated.
the 5th column will be L representing the light.
T means True means the light is on.
F means False means the light is off.
Here's what your truth table would look like if constructed this way.
U1 D1 U2 D2 L
T F T F T
T F F T F
F T F T T
F T T F F
if the implication is that when a switch is not in the up position, then it has to be in the down position, we can simplify the truth table to be as follows:
U1 U2 L
T T T
T F F
F F T
F T F
U1 being true means that switch 1 is in the up position.
U1 being false means that switch 1 is in the down position.
Similarly for U2
the logic statements for this truth table would look like:
U1 & U2 => L
this means that the state of U1 and the state of U2 both define the state of L.
Hopefully this is what you are looking for, or at least something similar to it.
