Fallacies
Denying the Antecedent

 Definition 

Also called Confusing A Necessary With A Sufficient Cause.

Any argument of the following form is invalid: If p1 then p2; not-p1; therefore, not-p2.

 Explanation 

This is mathematically incorrect. p1 is a sufficient cause of p2 and that means that if we have not-p2, we can conclude that we have not-p1 (the negation of "if p1 then p2"). But having not-p1 is not enough to conclude that we have not-p2.

 Examples 

If you get hit by a car when you are six then you will die young. But you were not hit by a car when you were six. Thus you will not die young.
Of course, you could be hit by a train at age seven, in which case you still die young.

If I am in Calgary then I am in Alberta. I am not in Calgary, thus, I am not in Alberta.

 Counter-examples 

None.

 Advices 

Show that even though the premises are true, the conclusion may be false. In particular, show that the consequence p2 may occur even though p1 does not occur.