Introduction to Proposition Logic

On this page, I will use capital letters, such as P and Q to refer to statements, which have a "truth value" -- that is, they are true or false.

If I write, simply,

P

this means the same thing as

P is a true statement.

That is, asserting P is the same thing as asserting that P is true.  If P means "it is a sunny day", then asserting P is the same as asserting that it is a sunny day.  It is unnecessary to say "it is true that it is a sunny day".

"not P" means the same thing as "P is false".

Argument Forms

Modus Ponens

If P then Q.
P.
therefore Q.

Modus Tolens

If P then Q.
not Q.
therefore not P.

Disjunctive Syllogism

P or Q.
not P.
therefore Q.

Disjunction Elimination, or proof by Cases

P or Q.
If P then R.
If Q then R.
therefore R.

Hypothetical Syllogism

If P then Q.
If Q then R.
therefore, If P then R.

Internet References

Related pages in this website

Basic Principles

Truth Value -- a discussion of "truth tables" as a way of illustrating the meaning of logical operations

The webmaster and author of the Math Help site is Graeme McRae.
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