True-False Practice with Quantifiers

These are just for practice and don't affect your grade. They are intended to be pretty easy, just a quick way to get used to the notation. For maximum effect, compare and constrast them, try to prove your answers, etc. I'm assuming you've had a few MAA 3200 lectures or have read Ch 2 of Velleman's book. Assume the universal set is U = R.

One of the questions is not quantified correctly, but you might not even notice. See if you can find it, and fix it by inserting a ".

True False. $ x, x Î [2, 6] Ù x Î [7, 10].

True False. $ x, x Î [2, 6] Ù $ x, x Î [7, 10].

True False. $ x, x Î [2, 6] Ú x Î [7, 10].

True False. " x, Ø (x Î [2, 6] Ù x Î [7, 10])

True False. $ y, " x, x < y.

True False. " x, $ y, x < y.

True False. Ø($ y, p(y)) Û " y( Øp(y)).

True False. If A Í B, then " x, x Î A ® x Î B

True False. $! x, x 2-1 = 3.

True False. $! x, x -1 = 3.

1) The small error is in #8. It should begin with " " sets A and B..."
2) If you can't do the quiz because you have forgotten some notation, you need to read your book again. But here's a cheat list of the main symbols used above: Û logically equivalent, ® implies, Î in, " for all, $ exists, Í contained in, Ø not, Ú or, Ù and, ! unique.
3) If you find this page useful (or difficult), I would like to hear from you.

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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.

å¥ £ ³ Í » ^Û | A-1 c2 v2® ΠżÇÈa/b ||"$ Í Øp \B Æ ¹ ÚÙÞ«D