Truth Tables

Given the truth table below defined for the operation *, answer the following questions:

p | q | p*q
-----------
T | T | F
T | F | F
F | T | T
F | F | F

a.) Determine whether * is an associative operation (ie., does (p*q)*r = p*(q*r)? Use the truth table, explain.

b.) Determine whether * is a distributive operation (ie., does p*(q v r) = (p*q) v (p*r). Use the truth table again.

c.) Express p*q in terms of p, q, ^, v, ~ (note that not all of them have to be used)

d.) Express p -> q in terms of p, q, ~, * (no others are used)

$\displaystyle c)\quad \left( {p*q} \right) \equiv \left( { \sim p \wedge q} \right)\quad \& \quad d)\quad \left( {p \to q} \right) \equiv \sim \left( {q*p} \right)
$

You must do the others. They are just too tedious.