Let F2 = {0, 1}. Define addition and multiplication on the set F2 by the following rules:

x + 0 = x,

x 0 = 0

1 + 1 = 0,

1 1 = 1

for all x F2. Complete parts (a) and (b) below: (a) Prove that F2 is a field (the finite, or Galois, field of two elements).

(b) Show that F2 is not an ordered field.