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Given the statement, "If you do not like this book, then you do not like mathematics," what is the converse, inverse, and contrapositive?
Question
#106196. Asked by jakesgirl88. (Jun 09 09 5:56 PM)
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daBomb619
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Converse: "If you do not like mathematics, then you do not like this book."
Inverse: "If you like this book, then you like mathematics."
Contrapositive: "If you like mathematics, then you may like this book."
 http://www.jimloy.com/logic/converse.htm
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looney_tunes
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In the converse of a proposition, the subject and predicate are reversed. (In symbols, a -> b becomes b -> a.) The converse of this statement is "If you do not like mathematics, then you do not like this book".
http://en.wikipedia.org/wiki/Converse_(logic)
The inverse of a proposition is formed by negating (adding or removing 'not' to/from) both subject and predicate. (In symbols, a -> b becomes ~a -> ~b.) The inverse of this statement is "If you like this book, then you like mathematics".
http://www.regentsprep.org/rEGENTS/MATH/relcond/Linvers.htm
The contrapositive of a proposition is formed by negating both subject and predicate, and reversing their positions in the proposition. (In symbols, a -> b becomes ~b -> ~a.) In thie case, the contrapositive is "If you like mathematics, you like this book".
http://en.wikipedia.org/wiki/Contraposition
It should be noted that only the contrapositive is ;logically equivalent to the original proposition. That is, if the original proposition is true, so is the contrapositive. This is not necessarily true of the converse and inverse.
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