Law of the Double Negation

Rule:	~(~P)

	=>	P

Examples using the Law of the Double Negation

The following are VALID using the Law of the Double Negation:

It is not the case that Sylvia will not teach tomorrow.
=> Sylvia will teach tomorrow.
It is not true that Brian will not hang around with friends this upcoming weekend.
=> Brian will hang around with friends this upcoming weekend.
It is not the case that Polina does not plan to ace the midterm next week.
=> Polina plans to ace the midterm next week.

Counter Examples using the Law of the Double Negation

The following are INVALID using the Law of the Double Negation:

It is not the case that Suzan has to work this upcoming Sunday. Therefore, Suzan has to work this upcoming Sunday.
=> This is INVALID. We should have 2 negations. Incorrect conclusion.
It is the case that Sheela does not plan to do any aerobics this weekend. Therefore, Sheela plans to do aerobics this weekend.
=> INVALID. Again, need 2 negations. Incorrect conclusion.
It is the case that Sylvia has Open House in school next week. Therefore, Sylvia does not have Open House at school next week.
=> INVALID. No negations at all in first statement. Incorrect conclusion.

Interactive Question #1

It is not the case that Brian does not plan to take off of work next week. So....

Brian plans to take off of work next week.
Brian plans not to take off of work next week.
Brian plans to work very hard next week.
Brian hates work.

Interactive Question #2

It is not the case that Polina does not like the American Pizza. So, we can conclude that Polina hates the American Pizza.

Valid
Invalid

Interactive Question #3

If "Sheela went to the library" is the conclusion, what must the hypothesis be?

Sheela went to the zoo.
Sheela went to the bank.
It is not the case that Sheela did not go to the library.
Sheela went to Borders.

Interactive Question #4

The conclusion is: P
The hypothesis must be what?

Click here for MORE Interactive Questions