Precalc0001to0005-page13 - p ± q ² ~ q ± ~ p • This...

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(Section 0.2: Logic) 0.2.4 PART D: CONVERSE, INVERSE, AND CONTRAPOSITIVE The converse of p ± q is: q ± p The inverse of p ± q is: ~ p ± ~ q • “~” and “ ¬ ” are used to denote “not.” They are negation operators . The contrapositive of p ± q is: ~ q ± ~ p TIP 1 : Take the original statement, switch the propositions, and negate them. Contrapositive Theorem If an “if-then” statement is true, then its contrapositive must be true, and vice-versa. In other words, they are logically equivalent . That is,
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Unformatted text preview: p ± q ( ) ² ~ q ± ~ p ( ) . • This can be proven using truth tables in a discrete mathematics class. As a result, any “if-then” theorem you know to be true has a contrapositive associated with it that will automatically be true. WARNING 3 : An “if-then” statement may or may not be logically equivalent to its converse or its inverse. (However, the converse and the inverse must be logically equivalent to each other. Why? How are they related?)...
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This document was uploaded on 12/29/2011.

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