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 Logical connectives (Posted on 2012-01-24)
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)

 See The Solution Submitted by Math Man Rating: 4.5000 (2 votes)

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 NOR | Comment 5 of 6 |
`   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

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