May 2024
Intermediate to advanced
332 pages
15h 45m
English
Content preview from Discrete Mathematics
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---------------------------SYMBOLIC
LOGIC
75
biconditional gates also? The answer is no. For implication (that is, for
~
),
the reason is that this operator is
not commutative that is,
(p
~
q) is not logically equivalent to (q
~
p). This means that
if
an implication gate
did exist, we would have to be careful about attaching the wires to the inputs
of
such a gate.
If
we get them
reversed we get a different answer. Instead
of
computing
(p
~
q), we might be computing (q
~
p)
.
It is also not clear what it would mean
if
we had a three-input implication gate. Since
~
is also not
associative, we would have to choose either to make it mean
((p
~
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