SET020 · Sets, relations & logic · Classes 11–12
De Morgan laws
De Morgan's laws turn the negation of an AND into an OR of negations, and vice versa. They hold for sets too: (A ∪ B)′ = A′ ∩ B′.
¬(p ∧ q)De Morgan laws
📐 Formula
¬(p ∧ q) = ¬p ∨ ¬q; ¬(p ∨ q) = ¬p ∧ ¬q; (A ∩ B)′ = A′ ∪ B′
✏️ Worked example
p = T, q = F: ¬(p ∧ q) = ¬F = T and ¬p ∨ ¬q = F ∨ T = T. Equal, for every choice of p and q.
🌍 Where it is used
Simplifying conditions in programs and circuit design.
❓ Quick check
¬(p ∨ q) equals…
🏋️ Practice
EasyNegate: 'It is hot and sunny.'
Answer: It is not hot or not sunny.
Medium(A ∪ B)′ = ?
Answer: A′ ∩ B′
ChallengeCheck ¬(p ∧ q) = ¬p ∨ ¬q for p = q = T.
Answer: F = F ✓