Can any one explain de morgan's law of logic to me?

Answer 1

http://en.wikipedia.org/wiki/De_Morgan%27s_laws

To give some intuition, suppose P is true if and only if it is raining and Q is true if and only if you are wearing a raincoat outdoors. If you never go in the rain without a raincoat, then it can't be that P is true and Q is false. Thus, the following formula is true:

not(P and (not Q))
On the other hand, another way of expressing the same statement is that either:

It's not raining, so you don't care whether you're wearing a raincoat or not;
You're wearing a raincoat, so you don't care whether it's raining or not.

Answer 2

I'm not sure I can fully give you examples, but the basics are kind of interesting.

Put two statements together that somehow fit together, that is called a conjunction of statements.

Two statements that don't go together, that is called a disjunction of statements.

Now we apply the principle of paradox.

Negating two conjunction statements is the equivalent of disjunction of statements.

Negating two disjunction statements is the equivalent of a conjunction of statements.

We commonly say in English speech that a double-negative will make a positive. "There ain't [is not] no good thing" is equal to "There is a good thing". One teacher was describing that and said that in another language (reportedly Russian, but I don't know the fact of that), "Two positives will make a negative, but we do not have that in English." Suddenly a student the back of the class muttered the classic sarcasm, "Yeah, right." Idiomatically, that is two positives that make a negative.