How can “and” be defined using “not” and “or” in propositional logic?

In propositional calculus, the logical operator "and" (conjunction) can be defined using "not" (negation) and "or" (disjunction) through De Morgan’s laws.

According to these laws, the conjunction of two propositions, $p$ and $q$, is equivalent to the negation of the disjunction of their individual negations. Symbolically, this is expressed as:

$$p·q\equiv ~(~p\vee ~q)$$

In this formula:
* $~$ represents the negation operator ("not").
* $\vee$ represents the disjunction operator ("or").
* $·$ represents the conjunction operator ("and").

This relationship demonstrates that the truth value of a conjunction is determined by the truth values of its components, allowing complex logical statements to be transformed into alternate, often more convenient, forms.12