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)

1. ~P  = P|P
2. P&Q = (P|P)|(Q|Q)
3. PVQ = (P|Q)|(P|Q)
4. P->Q = ((P|Q)|(P|Q))|(Q|Q)
5. P<->Q = ((P|P)|(Q|Q))|((P|Q)|(P|Q))

Posted by Dej Mar on 2012-01-24 11:12:04