Possible error in study guide Ch 5?

See chapter 5 in the study guide, top of page 173 that relates to question 6 of page 221 of the prescribed text book.

Consider (v1 o v2 o v3)(x) = y

v3 would map x to say w, so that (x, w) is an element of V3
v2 would map w to say z, so that (w, z) is an element of V2
v2 would map w to say z, so that (z, y) is an element of V1

Or equivalently

V1(v2(v3(x))) = V1(v2(w)) = V1(z) = y.

My point is that the function on the RHS gets applied first, so it's right to left, not left to right as the question solution seems to suggest.

Also, the solution to the question appears to be inconsistent with the definition of o which is given on page 190 and the theorem on page 202.

I would appreciate a response by one of the lecturers, or a fellow student... Have I missed the plot or is there a genuine faux par in the study guide?

Kind regards,

Richard

Yes you are correct-well spotted.
Of course, from the def on p 190 we see that SoR means that R is followed by S,
so if (x,y)ESoR then for some w we have that (x,w)ER and (w,y)ES.

Relate this to the example solution top p 173 in the guide, then we can think of S as V1 and R as (V2oV3)
So if we start the proof
(x,y)EV1o(V2oV3), then this means that (V2oV3) is followed by V1,
so for some wEX we have (x,w)E(V2oV3) and (w,y)EV1
etc.
We will give the full solution in tut letter 203.

In your letter you have the following:
v3 would map x to say w, so that (x, w) is an element of V3
v2 would map w to say z, so that (w, z) is an element of V2
The next line should be
v1 would map z to say y, so that (z, y) is an element of V1

Many thanks for getting back to me.

Kind regards,
Richard