\
is a set of sentences including the logically false sentence P.
(for
contradiction) that \ is consistent.
by the definition of consistency, it is possible that all members of \
be true together.
P, a member of \, is
possibly true. But that means that P is not logically false. However,
we are supposing from the beginning that it is logically false!
our
assumption (in red) leads to a contradiction. That assumption is wrong, so \
is inconsistent after all.
Suppose
that __________
Assume
__________
Then, __________
So,
it follows that __________
Thus
__________
1.4ex III
More Informal Proofs
Matching. Drag sentences from the right to the correct
location in the proof box. Don't print until you've come to
the final page of this exercise.
First show that...
1. If some member of a set of sentences is logically false (i.e., selfcontradictory),
then that set is inconsistent.
Prove this by our indirect means of "reductio ad
absurdum". (That is, you will show an assumption wrong by showing
it leads to contradiction.)
