De Morgan’s Laws
Negation swaps AND and OR.
Key idea
Negation swaps AND and OR.
In depth
¬(p ∧ q) ≡ ¬p ∨ ¬q and ¬(p ∨ q) ≡ ¬p ∧ ¬q. To negate a compound, negate each part and swap and with or. Set versions: complement of A ∪ B is A′ ∩ B′.
Worked example
Not (tall and fast) means not tall, or not fast.
Formula
Real-world uses
- Rewriting negated search queries and code conditions, such as “not (A and B)” as “not A or not B”
Common mistake
Negating the parts but keeping the connective unchanged.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is De Morgan’s Laws?
Negation swaps AND and OR. It is a topic at the advanced level in Discrete Math & Number Theory.
What is the formula for De Morgan’s Laws?
The key formula is ¬(p∨q) = ¬p∧¬q.
Where is De Morgan’s Laws used in real life?
Real-world examples: Rewriting negated search queries and code conditions, such as “not (A and B)” as “not A or not B”.
What should I learn before De Morgan’s Laws?
Make sure you are comfortable with Logical Equivalence, the previous topic in Discrete Math & Number Theory.
What is a common mistake with De Morgan’s Laws?
Negating the parts but keeping the connective unchanged.
How can I practise De Morgan’s Laws?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after De Morgan’s Laws?
Move on to Converse and Contrapositive next.
Related advanced topics in Discrete Math & Number Theory
- Tautologies and Contradictions – Always true or always false statements.
- Logical Equivalence – Statements with identical truth tables.
- Converse and Contrapositive – A conditional equals its contrapositive.
- Quantifiers – “For all” and “there exists”.
- Negating Quantified Statements – Flip the quantifier and negate the predicate.
- Proof by Direct Argument – Derive the conclusion from premises with valid steps.