A common method to establish is through proof by
contradiction. As in direct proofs, we assume *p* is true but we also
assume the negation of *q* is true. From these facts, we deduce that
the negation of *p* is also true (or that *p* is false and hence the
contradiction). Our conclusion is that the original statement *q* must
be true. Logically we have
is equivalent to
.

A similar technique is known as reductio ad absurdum. Again, we wish to
establish . Suppose that we know *r* is a true statement.
As with proof by contradiction we assume *p* and the negation of *q* to
be true. Suppose we can now show that these imply that the negation of
*r* is true (or that *r* is false). We now have that *r* is both true
and false which is absurd. Our conclusion is that *q* is true.

Sun Sep 15 22:27:27 PDT 1996