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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)

daBomb619

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

 Jun 09 09, 6:06 PM
looney_tunes

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.

 Jun 09 09, 6:22 PM

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