Hint for Section G.1 Question 1

1. Check the group axioms:

• closure under multiplication: are the elements 0 * 0, 0 * 1, 1 * 0, and 1 * 1 in the set {0,1}?
• associativity: does (a * b) * c = a * (b * c) for a, b, c {0,1}?
• identity: do we have e {0,1} such that e * a = a = a * e for all a {0,1}?
• inverse: for all a {0,1}, do we have an a^-1 such that a * a^-1 = e = a^-1 * a?

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