# SOLUTION: how would you design a circuit for ahall light that has switches at both ends of hall such that the light can be turned on or off from either switch. I have to use this problem for

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 Geometry: Proofs in Geometry Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Geometry proofs Question 254834: how would you design a circuit for ahall light that has switches at both ends of hall such that the light can be turned on or off from either switch. I have to use this problem for this question Electrical circuits are designed using truth tables.circuit consists of switches. And wired in series as p^q. two switches wired in parallel can be use as p v q. Can you show me how to do this problem using the truth tableFound 2 solutions by richwmiller, Theo:Answer by richwmiller(9143)   (Show Source): You can put this solution on YOUR website!I moved the problem to logic out of geometry Answer by Theo(3464)   (Show Source): You can put this solution on YOUR website!a diagram of your switch could look like this: ``` A1 A2 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx battery xxxxxxxxxxxxxxx C1 C2 xxxx light xxxxx ground xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 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.