An algorithm is a sequence of steps to be followed to accomplish a certain task. Often used in computer programming, they can become interesting puzzles because even though there can be many ways to accomplish something, one may be better than another.
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)
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