Through the Looking Glass of Logic

Symbolic Logic These are problems from the Author of Alice in Wonderland, Lewis Carroll. His actual name is Dodgeson, and he was a mathematician professionally. His area of expertise is Symbolic Logic, and along with George Boole, developed this important area of mathematics.

The idea here is to come up with the ULTIMATE CONCLUSION from the statements given. For example:

  1. There are no pencils of mine in this box.
  2. No sugar-plumbs of mine are cigars.
  3. The whole of my property, that is not in the box, consists of cigars
From the (1) and (3) we can conclude that "All my pencils are cigars" Now we can use this together with (2) to reach the ULTIMATE CONCLUSION that "No pencils of mine are sugar-plumbs."

Seems strange, huh? well let's use symbols to help.

Symbol Description
PPencils
BBox
SSugar-plumbs
CCigars
Now we can re-write:
  1. No P in B.
  2. No S = C.
  3. All Not B = C.
From (1) we know that Any P must not be in B. But we know from (3) That All Not B is a C (none are P), therefore P=C.

From (2) we know that No S=C. Since we can substitute things that are equal, we can rewrite (2) as No S=P.

It takes a few times before you get the "hang of it." Try This one

< Previous   Next >