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For: (a OR b) AND (b OR c) IMPLIES a OR c

Value, a,b,c
True,T,T,T
True,T,T,F
True,T,F,T
True,T,F,F
True,F,T,T
False,F,T,F
True,F,F,T
True,F,F,F

The term "Value" means the validity (Truth value) of the statement as a whole. The other three, (one for each variable), are True or False values of the variables. The premise for the statement is, "If (a or b) and (b or c) are true or false, is (a or c) Truly or Falsely implied?

Thus, (a or b) and (b or c) implies (a or c) if and only if all the Values (operators and the varables) in the table are met. The value of the statement operator ' implication' is True for all but one condition; a=False, b=True, and c=False.

The statement can also be written as: a or b and b or c implies a or c.

This is not a finished work since the truth vaues of the other operators are not evaluated. "AND, OR" can also vary invalue making the table more complex. Example: Find the Truth values of the following...

OR, AND, IMPLIES, a, b, c

are six elements to evaluate. Three operators and three variables.

So, a truth table can get very complex.

A program that approaches this on a computer can be found (downloaded)

from: http://sourceforge.net/projects/logicaleval/

More Recources on the Web:

http://philosophy.hku.hk/think/

http://library.brooklyn.cuny.edu/