Law of Detachment (Modus Ponens)




Rule:

P => Q

P

=>

Q


Examples using the Law of Detachment (Modus Ponens)



The following statements are VALID using the Law of Detachment:
  1. If is is raining, Then you will get wet. It is raining. => You will get wet.

  2. If it is Wednesday, we have class. It is Wednesday. => We have class.

  3. If it is eight o'clock, Polina will have breakfast. It is eight o'clock. => Polina will have breakfast.


Counter Examples using the Law of Detachment (Modus Ponens)



The following statements are INVALID using the Law of Detachment:
  1. If it is late, Then Sylvia must be sleeping. Sylvia is sleeping. Then it must be late.
    =>This is INVALID. The premise and the conclusion have been interchanged.

  2. If it is Tuesday night, then Suzan is doing homework. Suzan is doing homework. Then it must be Tuesday night.
    =>This in INVALID. Again, the premise should not fall from the conclusion.

  3. If it is early in the morning, Then Brian will go to the Gym. Brian went to the Gym. Then Sheela went bowling.
    => This is INVALID. The third statement has nothing to do with the conclusion that follows.



Interactive Question #1


If it is Sunday, Then Sylvia goes to the library. It is Sunday, So...

Sylvia goes to the library.
Sylvia goes to class.
Sylvia stays at home.
Sylvia is tired.



Interactive Question #2


If it is raining, Suzan went to the circus. Suzan went to the circus. Then it must be raining.

Valid
Invalid



Interactive Question #3


If it is raining, then Sylvia must be baking. What must the hypothesis be if we know that Sylvia is baking?

It is snowing.
It is raining.
It is a sunny day.
It is night time.



Interactive Question #4


P => Q    ==>    Q    (In English, Given, "If P then Q" this leads to "Q")
What is the other hypothesis we need?




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