If you are stuck predicting how a circuit will work, make an assumption about how it works.  That's particularly helpful when only a couple of things can happen.

  Then, after you make an assumption, there will be some logical consequences of what you assume.  After you make your assumption, you need to check the consequences of the assumption you made.

  Often, when you check the consequences there will be implications about what you assumed.  At this point, you need to check to see if there are any contradictions.  If there are no contradictions they what you assumed could be true.

  At times it is possible to make an assumption that is the exact opposite of your original assumption.  If you assumed State A in your original assumption, assume State B and check the consequences.  Do the same for any other possible states.

   Check that out in logic circuits.  (Click here for an example.)  Flip-flops are examples of circuits that can exist in two different states, and it is difficult to analyze them directly.

   Check that out in diode circuits.  (Click here for an example.)  Diode circuits are examples of circuits where the method of contradiction can be used to good effect even though diode circuits are not usually capable of existing in two stable states.