** Next:** Implication
** Up:** Logical connectors
** Previous:** De Morgan Laws
** Contents**

**Definition 2.3.11**
A proposition which is always true is called a tautology.

The column of a tautology in a truth table contains only T's.
For example, if is a proposition, then
is a
tautology.
We could have used tautologies for proving all the previous laws; just
add an extra column to each truth table, corresponding to the specific
logical equivalence and check that this columns contains only T's.

**Definition 2.3.12**
A proposition which is always false is called a contradiction.

The column of a contradiction in a truth table contains only F's.
For example, if is a proposition, then
is a
contradiction.

root
2002-06-10