Constructing Truth Tables for Testing Sentences and Arguments

Truth tables are constructed in a way such that all the possible truth value combinations between atomic sentences are provided. Thus, a statement (or argument) with three atomic sentences will have an 8 line table. A statement or argument with 2 atomic sentences will have a four line table. Similarly, a statement with 4 atomic sentences will have a 16 line table. The construction of the table begins with the first atomic sentence being given the last assignment of truth values, and the last atomic sentence being given the first assignment of truth values. Thus, in the statement:

[-(A v -B) . C] <---> [(-A . B) . C]

the lines of the table are constructed such that

C is composed of the alternation of singular Ts and Fs in a vertical line.

B is composed of the alternation of double Ts and Fs in a vertical line.

A is composed of the alternation of quadruple Ts and Fs in a vertical line.

The table will then look like this:

A B C [-(A v -B) . C] <---> [(-A . B) . C]

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

Since the test in this case is to determine whether the statement is a tautology, a contingency, or a contradiction, the major value will be under the "<--->" sign.

In a statement such as: (-B v A) <---> (C . -B)

the alternation of truth values is like this:

B____ _A_ ____C