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# 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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