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)