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Math 3333 - Intermediate Analysis - David Blecher
Logic and deductive reasoning (Chapter 1, Lay)
The following will be a review for some, so we will move quickly. You probably will need to read
this carefully several times, as well as the additional discussion/examples in the textbook.
. Statement: a phrase that is either true or false, but not both. Mathematics consists
entirely of statements, and is thus either right or wrong. Be sure that your 'statements' are
properly written, and have meaning (make sense).
A statement which is true is also sometimes called 'valid', or is said 'to hold'.
. Example of a statement: 'Seven is an even number'. Example of a non-statement: 'This
sentence is false'. Or: 'Houston is a nice place to live'.
. Sometimes we give a statement a name. For example, let Q be the statement: Seven is an
odd number. Or, if x is a real number, let P(x) be the statement: x2 ?5x + 3 ? 0. Note
P(0) is true here, but P(1) is false.
. Where things live: In mathematics, it is very impo...

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