
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.