Loading...
Writing Proofs
A
B
C
D
E
F
. . . .

Deductive Reasoning and Proving

In summary, below are the steps in writing a direct proof.

1. Illustrate what is to be proven by drawing the necessary figure(s).
2. List the given statements. Write the conclusion that you need to prove.
3. Mark the figure(s) as needed, based on what you can deduce from the given statements.
4. Write all statements, including the simplest details, along with the reasons in a two-column table. Oftentimes, the first steps are the given statements and the last step is the conclusion that you need to prove.

There are cases when an indirect method of proving can be more easily done. The following are the steps in writing an indirect proof:

1. Assume that the conclusion is false.
2. Show that the assumption leads to a contradiction of the hypothesis or a known statement that is true.
3. Since the assumption about the conclusion is false, then the conclusion must be true.

To use the indirect method to prove the implication "if p, then q," assume the hypothesis p and the negation of the conclusion "not q."

Link these assumptions with definitions or other statements that are considered true to establish "if p and not q, then r." However, "not r" is known.

You arrive with a contradiction "r and not r." Therefore, the statement "if p, then q" is true.