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|p)|q)|((p|p)|q)

5. p<->q:  ((p|p)|q) | (p|(q|q))

Edited on January 24, 2012, 4:12 pm

Posted by Charlie on 2012-01-24 16:11:59