contrapositive

[kon-truh-poz-i-tiv] Logic.
adjective
1.
of or pertaining to contraposition.
noun
2.
a contrapositive statement of a proposition.

Origin:
1855–60; contraposit(ion) + -ive

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World English Dictionary
contrapositive (ˌkɒntrəˈpɒzɪtɪv)
 
adj
1.  placed opposite or against
 
n
2.  logic
 a.  a conditional statement derived from another by negating and interchanging antecedent and consequent
 b.  a categorial proposition obtained from another, esp validly, by any of a number of operations including negation, transferring the terms, changing their quality, and also possibly weakening from universal to particular

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Etymonline
Word Origin & History

contrapositive
1858 (implied in contrapositively), from L. contraposit-, pp. stem of contraponere (see contraposition).
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Identify and write the inverse, converse, and contrapositive of a given conditional statement and note the logical equivalences.
Indeed, elementary logic teaches that the contrapositive of a hypothesis is not necessarily true.
Identify the new statement as the converse, inverse, or contrapositive of the original statement.
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