Proving DeMorgan's Second Law

[Herricane]

Homework Statement

Use the first DeMorgan's law and the double negation law to derive the second DeMorgan's Law

Homework Equations

First DeMorgan's law is - (P and Q) is equivalent to - P or - Q

Negation Law is - - P is equivalent to P

Second DeMorgan's law is - (P or Q) is equivalent to - P and - Q

The Attempt at a Solution

I tried plugging in - - P for P. Should I do this for Q too? However this is not taking me anywhere.

 

[Herricane]

Never mind I found why I am doing it wrong. I need to start with

-P and -Q then use negation law
- [ -P and -Q]
- [ -(-P and -Q)] then use first law
- [ P or Q ] which is equivalent to -P and -Q !

 

[radou]

Unless I'm mistaken, you could prove this using a type of table with P, Q, P V Q and -(P V Q) at the top columns, and filling the columns with P and Q out with every possible combination of 0 and 1, and calculating the outcome. This table should then be equivalent to another table with P, Q, -P, -Q, -P & -Q at the top columns. i.e., for example, if P = 1 and Q = 0, the statements you with to prove should both equal 0.

Sorry if this was confusing.