Let P|Q mean "P and Q are both false." P|Q is true if P and Q are both false, and false otherwise. Define the following logical connectives just using P, Q, |, and parentheses.
1. ~P (not P)
2. P&Q (P and Q)
3. PVQ (P or Q)
4. P->Q (P implies Q)
5. P<->Q (P if and only if Q)
Truth table for | or NOR:
P Q P|Q
T T F
T F F
F T F
F F T
~ (not) in terms of | (NOR):
P ~P (P|P)
T F F
F T T
^ ^
& (and) in terms of | (NOR):
P Q P&Q (P|P)|(Q|Q)
T T T F T F
T F F F F T
F T F T F F
F F F T F T
^ ^
v (or) in terms of | (NOR):
P Q PvQ (P|Q)|(P|Q)
T T T F T F
T F T F T F
F T T F T F
F F F T F T
^ ^
-> (implies) in terms of | (NOR):
P Q P->Q ((P|P)| Q)|((P|P)| Q)
T T T F F T T F
T F F F T F F T
F T T T F T T F
F F T T F F T F
^ ^
<-> (iff) in terms of | (NOR):
P Q P<->Q ((P|Q)| P)|((P|Q)| Q)
T T T F F T T F F T
T F F F F T F F T F
F T F F T F F F F T
F F T T F F T T F F
^ ^
Note: NOR is commutative, but not associative.
Note: NOR and NAND are universal connectives -
All of the sixteen logical connectives
can be defined in terms of either.
|
|
Posted by Bractals
on 2012-01-24 16:27:58 |
NOR
