How do we consider the 'content' of a statement in propositional logic?

Question

From what I understand about formal logic, we are not concerned with the statements' content or our intuitive understanding of the content for that matter, but we are concerned with the statement forms or the way that the statements relate to each other.

Now please take a look at the picture taken from a book: (Discrete Maths & Its Applications by Susanna)

In the highlighted portions, the author is asserting that the statements are true or false based on the content alone. She is using the content's understanding of numbers to determine the truth values.

But isn't it against the principal of formal logic? I mean we can not determine the truth values or derive conclusions based on the content, right?

Please explain what is happening here.

Answer 1

The notion of "content" in propositional calculus is formalized with that of interpretation :

An interpretation of a truth-functional propositional calculus $\mathcal {P}$ is an assignment to each propositional symbol of the language of $\mathcal {P}$ of one or the other (but not both) of the truth values truth (T) and falsity (F), and an assignment to the connective symbols of $\mathcal {P}$ of their usual truth-functional meanings.

An interpretation of a truth-functional propositional calculus may also be expressed in terms of truth tables.

Thus, logical equivalence formalize the property of "having the same content".