Propositional Logic

You likely learned about the distributive property in your middle school algebra class. The distributive rule says that a term multiplied by two or more terms in parentheses is applied to each of those terms individually. For instance:

2(3 + 4) = (2)3 + (2)4 = 6 + 8 = 14.

In propositional logic, the distributive property is similar but with one key difference — logical connectives between terms must be flipped when the distribution takes place. In other words, each term is negated and any ands become ors and vice versa. More formally:

¬(P and Q) → ¬P or ¬Q

¬(P or Q) → ¬P and ¬Q

These rules are so important to propositional logic that the name of the long-dead British man that formalized them, Augustus De Morgan, was slapped on them. De Morgan’s Laws are often useful in rearranging statements or simplifying them for ease of understanding.