Solutions for Exercises in Unit 1
Exercise 2.2.4
We first show that the substructure generated by A contains the elements
̅ for
̅
. Let
̅ be such an element. If is formed by clause 1 of the definition,
then
̅ is in . If arises by clause 2, then
̅ is the result of applying a function
to some element already occurring in . This implies that
̅
.
On the other hand, every element of
is of the form
̅ by clause 1 of the definition
̅ for some ̅
of terms. If
, then
, so that is of the form
̅ by
induction and by clause 2 of the definition of terms.
Saylor URL: http://www.saylor.org/MA201 Subunit 1.2.2
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