# De Morgan's Law

*By Robert Laing*

What I took to calling *copula notation* because I read somewhere that the ∧ and ∨ symbols are called
copulas (but I can’t find the reference again) is a handy mnemonic for remembering two substitution
rules commonly called De Morgan’s Laws:

- ¬(p ∧ q) can be substituted with ¬p ∨ ¬q
- ¬(p ∨ q) can be substituted with ¬p ∧ ¬q

There’s an interesting relationship with set theory in that

- (P ∩ Q)
^{c}can be substituted with P^{c}∪ Q^{c} - (P ∪ Q)
^{c}can be substituted with P^{c}∩ Q^{c}

A handy feature of De Morgan’s Law is it isn’t just binary. It applies to any number of propositions:

p_{1} · p_{2}
· … · p_{i} =
p_{1} +
p_{2} +
… +
p_{i}