The rule for ~ is "If a T follows it, the result is F, and
if an F follows it, the result if T."
The rule for v is "If there is a T on either side of it, the result is T"
It is only F if there are F's on both sides.
The rule for ^ is "If there is an F on either side of it, the result is F"
It is only T if there are T's on both sides.
The rule for -> is "If it has T on the left and F on the right, the result
is F. Otherwise the result is T"
The rule for <-> is "If it has the same on both sides, the result is T".
If it has T's on both sides, the result is T.
If it has F's on both sides, the result is T.
If it has T on one side and F on the other side, the
result is F.
Put TTFF under A, and TFTF under B, and follow the above rules:
A | B | ~A |~B | Av~B | ~(Av~B) | ~A^B || ~(Av~B)<->(~A^B)
----------------------------------------------------------
T | T | F | F | T | F | F || T
T | F | F | T | T | F | F || T
F | T | T | F | F | T | T || T
F | F | T | T | T | F | F || T
Since the truth table came out with all T's on the right end, the
proposition is a tautology.
Edwin
