asserting the contrary or opposite; contradicting; inconsistent; logically opposite: contradictory statements.
tending or inclined to contradict.
noun, plural contradictories.
Logic. a proposition so related to a second that it is impossible for both to be true or both to be false.

1350–1400; Middle English < Late Latin contrādictōrius, equivalent to contrādic(ere) (see contradict) + -tōrius -tory1

contradictorily, adverb
contradictoriness, noun
intercontradictory, adjective
noncontradictory, adjective, noun, plural noncontradictories.
uncontradictory, adjective

1. irreconcilable, paradoxical. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
contradictory (ˌkɒntrəˈdɪktərɪ)
1.  inconsistent; incompatible
2.  given to argument and contention: a contradictory person
3.  logic contrary Compare subcontrary (of a pair of statements) unable both to be true or both to be false under the same circumstances
n , -ries
4.  logic a statement that cannot be true when a given statement is true or false when it is false

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

1530s, "mutually opposed, at variance," from L. contradictorius, from contradictorem, from contradicere (see contradiction). Meaning "fond of contradicting" is from 1891.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Malaria is a confounding disease-often, it seems, contradictory to logic.
Genius is the ability to hold two contradictory truths in the mind at the same
  time without going crazy.
It was because of the peculiarly contradictory way in which the capitalist
  system generated its fabulous wealth.
They present almost comically contradictory portraits.
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