Practice with Proof Strategies

These are just for practice and don't affect your grade. I assume you have read, pondered, and memorized Velleman, page 305, which summarizes some ideas from Ch 3. Below this paragraph I have listed some common strategies taken from that page. You are supposed to choose a correct strategy for each sentence-type in the quiz. For each question, only one of the strategies listed after it should be correct.

A) Assume p and prove q.
B) Prove p and q separately.
C) Prove p ® q and q ® p separately.
D) Find a value of x that makes p(x) true, and prove p(x).
E) Prove a) $ x, p(x) and b) " y, " z, (p(y) Ù p(z) ® y = z).
F) Let x be arbitrary and prove p(x).
G) Assume p is false and prove q.
H) Assume p is true and try to reach a contradiction.
I) Assume that q is false and prove p is false.
J) Assume a contradiction and try to prove p.
K) Assume p(x) and try to reach a contradiction.

The Questions:

p Ú q....... A D G

p ® q....... B H I

p ® q....... A F G

p Ù q........ A B I

Ø p........... A H J

$ x, p(x)... D F K

" x, p(x)... D F K

$ ! x, p(x) D E F

p « q....... A B C

(Ø p) ® q D G H

If you find this page useful, or difficult, I would like to hear from you. - S H.

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Written by S.Hudson, 8/03, using Javascript, and tth.exe to translate from TeX to HTML. If you want the HTML for any of the following math symbols, you can cut/paste from the source code of this web page.

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