1. Doing them:
Use an indirect proof to prove that the conclusion is true.
If p is an integer and p2 is divisible by 2, then p is divisible by 2. (Hint: An odd number can be written as 2n + 1, where n is an integer. An even number can be written as 2n.)
If a < b, then a + c < b + c.
If ac > bc and c > 0, then a > b.
(From McDougal & Littell's Algebra I, p. 703; a traditional text).
2. Writing about them; doing easy, concrete ones; and conducting interdisciplinary research:
Name and describe three forms of proof.
Prove that if 7x - 3 = 25, then x = 4. Write a two-column proof.
Research Edgar Allan Poe may be best known for his horror stories, including "The Pit and the Pendulum," and for his poetry, including "The Raven." He is also highly regarded as a lierary theorist and as a short story writer.
Edgar Allan Poe set out guidelines for the use of ratiocination in what was to become the modern detective story. Find out what he meant by ratiocination and how he used it in mystery stories such as "The Murders in the Rue Morgue."
(From McDougel and Littell's Integrated Math, p. 407; a reform text).