Complicating Sentences Using Logical Operators

Real-life situations

This lesson follows a consistent pattern for complicating sentences beyond simple propositions using logical operators. It shows the place of logical operators in natural language, then resolves both syntax and semantics of the new logical operator in the context of our binary logic language. The lesson begins with the logical NOT operator.

In natural language, we frequently encounter real-life scenarios where the use of negations with single propositions becomes essential. In everyday conversations, negations allow us to disagree with suggestions, such as expressing our preference by saying, “I don't want to go there.”

In the examples above, it’s evident that negations can help in opposing the original propositions.

Negation in formal logic

The negation is a fundamental logical operator that inverts the truth value of a given proposition.

Syntax

Given a proposition $P$, its negation is typically represented by a specific symbol or notation. The process of forming the negation of $P$ is denoted as $\neg P$. This indicates that if $P$ is true, then $¬P$ is false; and if $P$ ...