Precalc0001to0005-page12 - 2 x = 6 a proposition, even...

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(Section 0.2: Logic) 0.2.3 PART C: “IF AND ONLY IF” (OR “IFF”) STATEMENTS “If-and-Only-If” (Iff) Statements The statement “ p if and only if q ” can be written as “ p ± q .” If the statement is known to be true, we can write “ p ± q ,” or “ p ± q ”. • If p ± q , and if q ± p , then p ± q . • Then, the propositions p and q are logically equivalent ; either both are true, or both are false. Example 3 (An “If-and-Only-If” Statement) 2 x = 6 () ± x = 3 () . • We will call an equation such as “
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Unformatted text preview: 2 x = 6 a proposition, even though its truth value (true or false) depends on the value of x . Some sources differ. Definitions are essentially if and only if statements. For example, a number is a rational number if and only if it can be written in the form: integer nonzero integer True if and only if statements arise when an if-then statement and its converse are true....
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This document was uploaded on 12/29/2011.

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