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# hw1 - Math 300A&B Introduction to Mathematical Reasoning...

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Math 300A&B Introduction to Mathematical Reasoning Fall 2009 Assignment #1: Due Wednesday, 10/7/09 1. Eccles, p. 9, problems 1.2, 1.3. 2. A statement form is a sentence in which variables are used to represent propositions, such that it becomes a proposition when actual propositions are substituted for the variables. For example, if P and Q represent propositions, then P Q is a statement form. The truth value of a statement form depends on the truth values of the individual statement variables, and can be determined by a truth table. For example, the usual truth table for “and” determines the truth value of P Q . Two statement forms are said to be equivalent if they give the same truth value for all possible truth values of the statement variables that appear in them. For example, the following truth tables show that the statement forms P Q and Q P are equivalent: P Q P Q Q P T T T T T F F F F T F F F F F F Because the entries in the last two columns are identical, the two statement forms P

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hw1 - Math 300A&B Introduction to Mathematical Reasoning...

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