# What is the difference between logical statements and statement variables?

For the following two question

Let P, Q, and R be logical statements. Use a truth table to prove that_______.

Let P, Q, and R be statement variables, and suppose that the logical expression_______ is false.

The blank is two expressions which I don't know how to type those symbols, hope it doesn't matter.

## 2 Answers

Statement variables are atomic statements, i.e. statements with no connectives in them. Statement variables are usually written as letters $$p, q, r, \ldots$$.

Logical statements are any statements composed of statement variables and, possibly, connectives. For example: $$p$$, $$\neg p$$, $$p \land q$$, $$(q \lor p) \to (r \lor q)$$, $$\ldots$$.

Every statement variable makes for a logical statement, but not every logical statement is a single statement variable.

A logical statement like $$P$$ is meant to be a specific statement. For example, $$P$$ could mean 'It is raining'.

A statement variable is something we use to indicate that we are dealing with some statement ... but we don't know what it is.

It is like the difference between $$2$$ and $$x$$ when doing algebra. The $$2$$ is a specific number, but the $$x$$ is some unknown number.