Method

Making a Truth Table

Let p and q represent two different logical statements. Consider the following compound statement. p∨ q By making a truth table it can be determined for what values of p and q this statement is true and for what values it is false. There are three steps to follow to make a truth table for a compound statement.

Determine the Number of Columns

The number of columns in a truth table depends on the complexity of the compound statement. First, break the statement down into its simplest components. In this case, the compound statement p∨ q consists of the simple statements p and q.

Create one column for each simple statement and for each intermediate compound statement needed to build the original statement. Order the columns from simplest to most complex, with the original statement in the final column.

p	q	p∨ q

Therefore, this truth table has three columns.

Determine the Number of Rows

The number of rows in a truth table depends on the number of simplest statements, or variables, in the compound statement. Here, the simplest statements are p and q. Simplest Statements p and q Each variable can be either true (T) or false (F). With two variables, there are four possible combinations of truth values.

p	q	p∨ q
T	T
T	F
F	T
F	F

The general rule is that a truth table has 2^n rows, where n is the number of variables.

Fill in the Truth Table

The final step is to fill in the remaining cells, working from the simplest statements to the compound statement. Start by filling in the truth values of p and q. Then, use the disjunction p∨ q to complete the final column.

p	q	p∨ q
T	T	T
T	F	T
F	T	T
F	F	F

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