Truth tables can determine which of the following?
Truth tables can determine the truth value of logical expressions or propositions, and they can help determine the validity of arguments in propositional logic. Specifically, truth tables can determine the following:
1. Whether a logical expression is a tautology: A tautology is a statement that is always true, regardless of the truth values of its individual components. By constructing a truth table for a logical expression and examining the resulting truth values, you can determine if it is a tautology. If all the rows of the truth table evaluate to "true" for the expression, it is a tautology.
2. Whether a logical expression is a contradiction: A contradiction is a statement that is always false, regardless of the truth values of its individual components. Again, by constructing a truth table for the logical expression and examining the resulting truth values, you can determine if it is a contradiction. If all the rows of the truth table evaluate to "false" for the expression, it is a contradiction.
3. Whether two logical expressions are logically equivalent: If two logical expressions always have the same truth value for all possible combinations of truth values of their individual components, they are considered logically equivalent. By constructing truth tables for both expressions and comparing the resulting truth values, you can determine if they are logically equivalent. If the truth values in each row of the truth tables are identical for both expressions, they are logically equivalent.
4. Whether an argument is valid: In logic, an argument is considered valid if it is impossible for all the premises to be true and the conclusion to be false. By constructing a truth table for the premises and the conclusion of an argument and evaluating the truth values, you can determine if the argument is valid. If there are no rows in the truth table where all the premises are true and the conclusion is false, then the argument is valid.