Contradiction When two claims are exactly opposite in such a way that they could neither both be true at the same time nor both be false at the same time.

 The truth of one entails the falsity of the other; the falsity of one entails the truth of the other: if it is true that all tigers eat flesh then is must be false to claim that some tigers do not eat flesh (compare these two statements visually on separate two circle Venn diagrams to see the contradiction by observing the shading and an x in the same region, region 1; note that if the x is false it is shaded out and shading is removed if the x is true; the case is similar in the relation of E-statements to I-statements as pictured on respective Venn diagrams). See the note under contrariness on full versus partial contradiction.

For further reflection, consider how much easier it is to see that two statements cannot be true at the same time than it is to see that they cannot be false at the same time.  It is easy to see that if "all P are D" is true, then "some P are D" must be false (and if "some P are D" is true, then "all P are D" cannot be true).  But it is more subtle to see how one of these statements being false entails the truth of the other.  Let's consider the entailments each way.  a) If the A statement is false, why does that imply the truth of the O statement?  Or, why is it the case that if "all P are D" is false then it must be the case that "some P are not D"?  Looking at region 2 on the graph may help us.  If it is false that all P are confined to region 2, then some, if not all, must be outside of region 2.  We cannot be sure that all are outside of 2 but we know for sure that some must be.  Hence, "some P are not D" is implied by the fact that "all P are D" is false.  b) If the O statement is false, if it is not the case that "some P are not D, then must it be the case that "all P are D"? Yes, again looking at the Venn diagram, notice that for this O statement to be false then all "P's" in region 1 (any x's in 1) must be shaded out of 1 and thus "moved" over to 2.  Region 1 is thus shaded and the diagram now says "all P are D."  

A lesson here is that study of the very notion of contradiction develops logical skill.  Exercises like this one may seem irrelevant to the practical concerns of life and the specific concerns of Christians learning and sharing the word of God with those in need.  However, this is no more irrelevant to workmanship in the word than is weight training to skill on a tennis court.  Some exercise is direct in its bearing on our skills in life and some exercise is less direct.  Both are needed. Likewise, many aspects of the study of logic involve the development of critical thinking tools (such as deepening one's grasp of the principles of a valid argument) and some aspects of the study of logic develop discipline of mind, discernment, and judgment (such as the exercise above regarding contradictory statements).  Time spent on these matters is time well spent in devotion to Christ.  This is part of the picture of loving God "with all your mind" (Matt.10:27). Of course, the indirect wisdom of God that we study in logic does not have the preeminence that belongs to the direct wisdom of God  that we study in Scripture.  But there is a sense in which it can be said that the study of logic has priority (for a season, say, in developing interpretive craftsmanship as part of theological training) in order that the study of Scripture may have preeminence.  In a word, it is simply like learning to read skillfully in order to read Scripture skillfully (cf. 2 Tim. 2:15).