Propositional logic is about reasoning with propositions. These are sentences that can be assigned a truth value: *true* or *false*. They are built from primitive statements, called *atomic propositions*, by using *propositional logical connectives*. The truth values propagate over all propositions through *truth tables* for the propositional connectives. In this chapter I explain how to understand propositions and compute their truth values, and how to reason using schemes of propositions called *propositional formulae*. I will formally capture the concept of *logically correct propositional reasoning* by means of the fundamental notion of *propositional logical consequence*.

The basic concept of propositional logic is **proposition**. A proposition is a sentence that can be assigned a unique **truth value**: true or false.

Some simple examples of propositions include:

- The Sun is hot.
- The Earth is made of cheese.
- 2 plus 2 equals 22.
- The 1000th decimal digit of the number is 9.
(You probably don't know whether the latter is true or false, but it is surely

*either true or false*.)

The following are not propositions (why?):

- Are you bored?
- Please, don't go away!
- She loves me.
- is an integer.
- This sentence is false.

Here is why. The first sentence above is a question, ...

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