Editing Modus tollens (section)

== Explanation ==
The form of a ''modus tollens'' argument is a mixed [[hypothetical syllogism]], with two premises and a conclusion:

:If ''P'', then ''Q''.
:Not ''Q''.
:Therefore, not ''P''.

The first premise is a [[Material conditional|conditional]] ("if-then") claim, such as ''P'' implies ''Q''. The second premise is an assertion that ''Q'', the [[consequent]] of the conditional claim, is not the case. From these two premises it can be logically concluded that ''P'', the [[Antecedent (logic)|antecedent]] of the conditional claim, is also not the case.

For example:

:If the dog detects an intruder, the dog will bark.
:The dog did not bark.
:Therefore, no intruder was detected by the dog.

Supposing that the premises are both true (the dog will bark if it detects an intruder, and does indeed not bark), it logically follows that no intruder has been detected. This is a valid argument since it is not possible for the conclusion to be false if the premises are true. (It is conceivable that there may have been an intruder that the dog did not detect, but that does not invalidate the argument; the first premise is "if the dog ''detects'' an intruder". The thing of importance is that the dog detects or does not detect an intruder, not whether there is one.)

Example 1:
:If I am the burglar, then I can crack a safe.
:I cannot crack a safe.
:Therefore, I am not the burglar.
Example 2: 
:If Rex is a chicken, then he is a bird.
:Rex is not a bird.
:Therefore, Rex is not a chicken.