A number of students have asked about the question in the first
weeks homework which asks to show that a * (b * c) = (a * b) * c.
The distributive law (Proposition 10) is very useful in proving this
identity, but in the notes it appears slightly after the assertion that a * (b * c) = (a * b) * c. However, by careful inspection of the proof of Proposition 10 we see that we are not actually using the associativity of multiplication in the proof. So you are permitted to use Proposition 10 in this question, as there is no danger of circular reasoning - but you should say this explicitly when you do your homework. Note, on the other hand, that it would be dangerous to use Proposition 10 to prove the other parts of Q4, since those parts are used in the proof of Proposition 10.
I'll modify the order of presentation in the notes so as to remove the apparent circularity.
Terry