Final answer:
A truth table is constructed by listing all possible combinations of the variables and determining the truth value of the statement for each combination. Based on the truth values, we can determine if the statement is a tautology, contradiction, or neither.
Step-by-step explanation:
A truth table is a table that shows the truth values of a logical expression for all possible combinations of its variables. To construct a truth table, we list all possible combinations of the variables and determine the truth value of the expression for each combination. Based on the truth values, we can determine if the statement is a tautology, contradiction, or neither.
To illustrate, let's say we have a statement represented by the variables P and Q. We construct a truth table by listing all possible combinations of P and Q, and then determine the truth value of the statement for each combination.
PQStatementtruetruefalsetruefalsetruefalsetruefalsefalsefalsetrue
In this case, the statement is neither a tautology nor a contradiction since it has both true and false values in different rows of the truth table.