Question 254834
a diagram of your switch could look like this:


<pre>


                      A1                             A2
                      xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

battery xxxxxxxxxxxxxxx  C1                      C2  xxxx light xxxxx ground

                      xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                      B1                             B2
</pre>
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.


<pre>

                       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
</pre>
if we let:


C1 to A1 = UP
C1 to B1 = DOWN
C2 to A2 = UP
C2 to B2 = DOWN


then the table becomes:


<pre>

                       switch 1              switch 2           light

                       UP                    UP                   ON

                       UP                    DOWN                 OFF
                       
                       DOWN                  DOWN                 ON

                       DOWN                  UP                   OFF
</pre>
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.

<pre>
                        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
</pre>
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:


<pre>
                        U1  U2  L
                        T   T   T
                        T   F   F
                        F   F   T
                        F   T   F
</pre>
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.