Contradiction of a statement? My textbook has asked me to find the "contradiction" of a given statement but I have not learned to do such a thing and googling has not yielded in any results whatsoever. Exactly what is the contradiction of a statement and how to form it, given any statement? 
Edit: This is the problem in question:

"Write the converse, contrapositive and contradiction of the statement "If ∆ABC is right angled at B, then AB²+BC²=AC²"

The answer for the contradiction of this statement is given as 

"∆ABC is right angled at B and AB²+BC²≠AC²"

 A: What you seem to be asking, when you (your text) refers to the "contradiction" of a statement, might be better termed as the "negation" of a sentence. For example, if person A declares $p$, another person B would be contradicting A by declaring "not $p$. That is, person B is asserting the negation of $p$.
So, we have a sentence we'll call $p$.  It's negation is simply $"\lnot p".$
So if we know that $p$ is true, its negation would be false.
If the sentence (proposition), for example, is "$x$ is an odd number", it's negation would be "it is not the case that $x$ is an odd number," or equivalently, its negation would be "$x$ is an even number."
A: a contradiction is a statement which is always false,  like P and notP.
for example if we have a<1  and we find that a>1, there is a contradiction.
a statement whis is always true is called a tautology ( tautologie in french).
for example :
the square of a real is positive.
A: Let's use formal approach.
Let $$A = \text{∆ABC is right angled at B},$$
$$B = \text{AB²+BC²=AC²}.$$
Then your first statement is $A \to B$ that is equal to $\neg A \vee B$. The contradiction (using de Morgan's theorem) is $\neg(\neg A \vee B) = A \& \neg B$. And this stands for exactly '∆ABC is right angled at B and AB²+BC²≠AC²'.
A: But the original post asked for the contradiction of a statement, not just a statement that "is" a contradiction.
