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From: Mitchell Hockley on 2 Jun 2010 06:03
Hi,

Could anyone help me with this question (from Bostock's Intermediate
Logic)

"The theory of groups can be presented as having in its vocabulary
just identity and a single two-place function f(x,y) which we write as
'x.y'. The usual laws for identity apply, and in addition these three
axioms:"

(A1) Axyz(x.(y.z) = (x.y).z)

(A2) AxyEz(x = z.y)

(A3) AxyEz(x = y.z)

Prove:

a = a.c |= c = c.c

(Hint: Use Ez(c = z.a))

Thanks for any help,
Mitch.
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