Law of Modus Tollens




Rule:

P => Q

~Q

=>

~P


Examples using the Law of Modus Tollens



The following are VALID using the Law of Modus Tollens:

  1. If it is a sunny day, then Polina will go hiking. Polina will not go hiking.
    => Then it must not be a sunny day.

  2. If it is a hot day, then Brian will wear shorts. Brian is not wearing shorts.
    => Then it must not be a hot day.

  3. If it is a humid day, then Suzan will be thirsty. Suzan is not thirsty.
    => It must not be a humid day.


Counter Examples using the Law of Modus Tollens



The following are INVALID using the Law of Modus Tollens:

  1. If it is a sunny day, then Polina will go hiking. It is not a sunny day. Therefore, Polina will not go hiking.
    => This is INVALID. You are given the negation of the premise. Cannot conclude anything.

  2. If it is a weekend, Sheela is doing aerobics. Sheela is not doing aerobics. Therefore, it must be a weekend.
    => INVALID. Need to conclude the negation of the premise.

  3. If it is Saturday, Then Sylvia is sleeping in. It is not Saturday. Therefore, Sylvia is not sleeping in.
    => INVALID. You are given the negation of the premise. Cannot conclude anything.



Interactive Question #1


If it is Fall, the leaves will fall. The leaves will not fall. So...

It must be Fall.
It is not Fall.
It must be Spring.
It must be Winter.



Interactive Question #2


If there is a sale, Sylvia will go shopping. If Sylvia did not go shopping, Then there wasn't a sale.

Valid
Invalid



Interactive Question #3


If there is a test, then Suzan will study. If the conclusion is: There wasn't a test, what is the hypothesis?

Suzan went to bed.
Suzan went out to dinner.
Suzan took the test.
Suzan didn't study.



Interactive Question #4


P => Q    ==>    ~P    (In English, Given, "if P then Q" leads to "Not P")
What is the other hypothesis?




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