1. A function from Boolean algebra B to Boolean algebra B∗ is a homomorphism if it satisfies the definition of isomorphism, but is not necessarily a bijection.

f(x+y)=f(x)&f(y) • f(x·y)=f(x)∗f(y) • f(x′) = (f(x))′′ (a) Prove f(0) = 0∗ (b) Give an example of a homomorphism from P({1,2,3}) to P({1,2}). (It will not be an isomorphism—why?)