## Strategy Menu:

# Contradiction Command

Use the Contradiction command if you want to do
a proof by contradiction. Select the goal that you want to prove by
contradiction and give the Contradiction command. Proof Designer will
create a subproof in which it is assumed that the goal is false, and then
it will say that you must prove a contradiction to complete the subproof.
The negation of the original goal will be added to the givens list, and
the new goal will be listed as “Contradiction”.

If you are working on a proof by contradiction and you think you know
which given you want to contradict, you can select it and give the
Contradiction command. Proof Designer will indicate that you have to
prove the negation of the selected given in order to arrive at the desired
contradiction.

You can combine these two uses of the Contradiction command in one
step: If you want to do a proof by contradiction and you know right from
the start which given you want to contradict, select the given and give
the Contradiction command. Proof Designer will create a subproof in which
it is assumed that the goal is false, and then it will say that you must
prove the negation of the selected given to arrive at a contradiction.