These are two of the simplest argument patterns.  We use them in everyday life all the time.

Modus ponens

          If Picasso painted ‘Guernica’ then he was a great artist.

          Picasso painted ‘Guernica’.

          Therefore, he was a great artist.

     

Modus tollens 

         If there is life on Mars we’d have found evidence of it.

         We have not found evidence of it.

         Therefore, there is no life on Mars.


 

Both the above arguments are valid.  If the premises are true, the conclusion must be true.  If you disagree with the conclusion that must be because you think one of think one of the premises is false.

Sometimes people construct arguments that look a bit like modus ponens and modus tollens but which are actually mistaken, invalid argument patterns.  These mistakes are so common, though, that logicians have given the fallacies names.

          Fallacy of affirming the consequent  [invalid]

            If Lincoln committed suicide then he’s dead.

            He’s dead.

            Therefore, he committed suicide.        

                                            

           Fallacy of denying the antecedent  [invalid]

              If Lincoln committed suicide then he’s dead

              He didn’t commit suicide.

              Therefore he’s not dead.

The arguments are clearly fallacious because although the premises are true, the conclusions are obviously false.