A proposition is a statement that is either true or false, but not both. It must have a definite truth value. Propositions are the building blocks of logic and mathematics.

Example 1

A simple example is the statement:

• "It is raining."

This statement is a proposition because it can be either true or false, depending on the weather.

If we let $p$ represent this proposition, we can write:

Example 2

In mathematics, a proposition can be a statement like:

• "The number 5 is greater than 3."

This is also a proposition because it is either true or false. In this case, it is true.

If we let $p$ represent this proposition, we can write:

Propositions are fundamental in logic, as they allow you to construct more complex statements and reason about their truth values.

Not a proposition

A statement that is not a proposition is something that cannot be clearly labeled as true or false. For example:

• Questions are not propositions.
  Example: "What is your favorite number?"
  You can’t say this is true or false—it’s just a question.
• Commands are not propositions.
  Example: "Solve this equation."
  This isn’t true or false either—it’s an instruction.
• Statements with unclear meaning are not propositions.
  Example: "This statement is false."
  If you think about it, this creates a paradox. If it’s true, then it’s false, and if it’s false, then it’s true. It doesn’t work as a proposition.