Subject: Re: Approach to logic problems
Date: Thu, 2 Oct 1997 17:22:49 -0400
From: Alex Bogomolny
It's all Boolean Algebra although sometimes the straightforward application is awkward.
Statements are about something. Let this somethings be A,B,C,...
That A is claimed to be true is denoted as A
That A is claimed to be wrong is denoted as -A
A statement might,e.g, be "A and -B".
The first gave 4 statements: a1, a2, a3, a4, only two of wich are true. What's then true is
1: (a1 and a2 and -a3 and -a4) or (a1 and -a2 and -a3 and a4) or ... (There are six pairs of parentheses.)
Thus you have 4 composite statements. You may combine them with and
1: and 2: and 3: and 4:
Remove parantheses using distributive laws:
(a or b) and c = a and c or b and c
By convention, "and" binds stronger than "or". Also use,
a and -a = false
a or -a = true
a and true = a
a or true = true
a and false = false
a or false = a
With all this theory, you may want to detect impossible
or obviously true combinations at the ouset. Then use
the above to simplify starting set of statements.