Lugo should have put the steps in reverse order or at least
mention that each step is reversible. He has reversible steps in
each of his examples. This corresponds to each statement being
equivalent to the next. This is logically the same as saying
that if A,B,C,D are statements then we have A <=> B <=> C <=> D.
This being the case, we can start with A and get D and we can
also start with D and get A. But if we want A => D then to avoid
being misleading to others we should start with A and get D. If
one of these <=> breaks down; that is, only goes one way, say B
<= C, then we can only derive D => A but not A =>D. Bob Bundy,
The example you gave of 1=2 thus 2=1 thus 3=3 is a great
example. The first conclusion that 2=1 is F following from F.
The second conclusion 3=3 is T following from F. So it is clear
that from a False statement we can logically derive either True
or False statements. This follows from the truth table for
implicaton (=>). p q p=>q T T T T F F The implication being True
corresponds to a VALI