De Morgan's Law

De Morgan's Law is a principle in mathematical logic that expresses the negation of a conjunction or disjunction in terms of negations of its individual components. It states that the negation of a conjunction (and) is equivalent to the disjunction (or) of the negations of its individual components, and the negation of a disjunction is equivalent to the conjunction of the negations of its individual components.

In symbolic notation, De Morgan's Law can be expressed as follows:

- ¬(p ∧ q) ≡ ¬p ∨ ¬q (negation of a conjunction)
- ¬(p ∨ q) ≡ ¬p ∧ ¬q (negation of a disjunction)

For example, if p represents "It is raining" and q represents "I am indoors", then the negation of the conjunction "It is raining and I am indoors" would be "It is not raining or I am not indoors" (¬p ∨ ¬q), and the negation of the disjunction "It is raining or I am indoors" would be "It is not raining and I am not indoors" (¬p ∧ ¬q).

De Morgan's Law is a useful tool for simplifying logical expressions and proving the equivalence of different logical statements.