Monaisia Livingston, Nikiray Colon

DeMorgan’s Law & Law of Detachment

De Morgan’s Law also known as DeMorgan’s Theorem is a law that deals with double negation. The relationship that deals with the double negation is known as DeMorgan’s duality. When DeMorgan’s Law is applied the conjunction or disjunction becomes the opposite. The Law of Detachment states that if the conditional is true than the hypothesis is true. If the hypothesis is true then the conclusion is true. Both laws can be represented symbolically.

1. ~ (~P^~Q) = P or Q
2. ~ (~P^Q) =P or ~Q
3. ~ (~P or ~Q) =P^Q
4. P→Q
P___

5. Q→P
Q______




1. ~(~p ^~(~Q))=
2. ~(~Q v ~(~P))=
3. P-Q
P__
4. Q ^~p=
5. ~(~Q v ~P)=
6. ~(Q v~(~P))=
7. p ^~Q=
8. ~Q v ~P
9. Q-P
Q______

10.Q-s
Q_

Conclusion: This is demorgan’s law and Law of detachment. Now you know how it works so show your magic and solve these problems. You shouldn’t have trouble now that you’ve seen the examples and read the intro. You always want someone to tell you the truth so think of that as law of detachment and just know that this law is always true