De Morgan's rules explained

Question

Could you please explain the De Morgan\'s rules as simply as possible (e.g. to someone with only a secondary school mathematics background)?

Answer 1

Looking over some of the answers, I think I can explain it better by using conditions that are actually related to each other.

DeMorgan's Law refers to the fact that there are two identical ways to write any combination of two conditions - specifically, the AND combination (both conditions must be true), and the OR combination (either one can be true). Examples are:

Part 1 of DeMorgan's Law

Statement: Alice has a sibling.
Conditions: Alice has a brother OR Alice has a sister.
Opposite: Alice is an only child (does NOT have a sibling).
Conditions: Alice does NOT have a brother, AND she does NOT have a sister.

In other words: NOT [A OR B] = [NOT A] AND [NOT B]

Part 2 of DeMorgan's Law

Statement: Bob is a car driver.
Conditions: Bob has a car AND Bob has a license.
Opposite: Bob is NOT a car driver.
Conditions: Bob does NOT have a car, OR Bob does NOT have a license.

In other words: NOT [A AND B] = [NOT A] OR [NOT B].

I think this would be a little less confusing to a 12-year-old. It's certainly less confusing than all this nonsense about truth tables (even I'm getting confused looking at all of those).