Hint for Section G.3 Question 1

1. We must check that the following properties hold.

For (Q,+):

• closure
• associativity
• commutativity
• identity
• inverse

For (Q-{0}, ·):

• closure
• associativity
• commutativity
• identity
• inverse

For all a,b,c in Q, a · (b + c) = a · b + a · c

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