Constructing a truth table for compound statements not only helps us to determine the possible truth values of that statement, but can also tell us something about the statement's logical structure. 

What is more, a truth table for compound statements reveals whether the truth of the statement depends on the specific truth values of its components or the logical form or structure of the entire statement. 

We can classify even the most complex compound statements in the following ways (Notice in the examples below that the determination of classification depends solely upon the truth values under the main logical operator):

TAUTOLOGY

All TRUE

SELF-CONTRADICTORY

All FALSE

CONTINGENT

≥1 TRUE & ≥1 FALSE

Similarly, truth tables may also be used to determine the relationship between multiple statements. 

This is valuable when considering the strength of an argument and how well various parts of the argument work to support one another. 

We can compare statements to one another in the following ways:

LOGICAL EQUIVALENCE

SAME values on each line

LOGICAL CONTRADICTION

OPPOSITE values on each line

LOGICAL CONSISTENCY

≥1 line both TRUE

LOGICAL INCONSISTENCY

0 lines both TRUE