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.
Good luck,
Alexander Bogomolny
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