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)