Students often fail to see the "beauty" of logic and truth values (tables).  They do not see a need for studying such "nonsense" and perpetually ask the question, "When are we ever going to REALLY use this?"  

Logic is one aspect of mathematics where the teacher can clearly show WHERE the material can be applied to the real world.  A simple understanding of electrical circuits is needed.  These necessary concepts can be easily grasped.

switch open :
no current

An open switch breaks the circuit.
This represents a FALSE condition.  
 

switch closed:
current

 A closed switch makes the circuit complete.
This represents a TRUE condition.  

 

Suggestion:
  Nothing beats hands-on experience!

Small electrical boards are manufactured for teaching concepts such as these.  They are relatively inexpensive.  

Stores such as Radio Shack™ sell the individual components (batteries, switches, lights, wire leads) needed to make your own "free-form" electrical boards (minus the board).

 

If  you are not able to use actual switches, lights, batteries and wires, you can still demonstrate the concept of logic and circuits by using magnets and pencil and paper drawings. 

Using your word processor and clipart (or by drawing freehand), create a set of chalkboard magnets to represent your switches, light and power supply.  You can quickly arrange them on the board and use chalk to represent the wiring.

Whether you use actual circuits, or you use magnets and drawings, the concepts can be presented in a similar manner.  The illustrations on this page will show actual circuits, but remember that you can accomplish the same process using paper and pencil.

 This is a simple circuit representing AND.  Notice how the path of the wire forms ONE complete circle.  BOTH switches must be pressed to allow the current to light the bulb (at the bottom).  Logically this circuit is
  (S1, S2 are the switches).

 

This is a simple circuit representing OR.  Notice how the path of the wire allows for the forming of TWO complete circles - one by following the yellow and white wires, the other by the red and white.  Pressing either (or both) switches will light the bulb.  Logically this circuit is

 

This circuit shows a combination of AND and OR.  There are TWO complete circles.  S1 and S3 will light the bulb.  S2 and S3 will light the bulb. 
 Logically this circuit is
  

You can arrange any patterns you wish your students to investigate.  You can assign a logical sentence and ask the students to arrange the circuits, or you can show a model and ask the students to determine the logical sentence.

You will be amazed at how quickly your students will grasp this concept of logic circuitry.  Most students have a good grasp of parallel and series circuitry from their Science classes. 

 For students who are having difficulty understanding truth values (or tables), this activity will give them a different perspective on the topic.