# Section 2.2: Problem 8 Solution

Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.

James R. Munkres

Assume that
is a set of sentences such that for any sentence
, either
or
. Assume that
is a model of
. Show that for any sentence
, we have
iff
.

By assumption, either every model of
is a model of
or every model of
is a model of
. Then, using the fact that no
can be both a model of
and a model of
, we conclude that

*every*model of is a model of ( ) iff*any*model of is a model of ( ). Note that does not actually require the assumption.