Thinking Mathematically (6th Edition)

The argument that contains two premises and a conclusion is given in a symbolic form is: $\left[ \left( \text{premise 1} \right)\wedge \left( \text{premises 2} \right) \right]\to \text{conclusion}$ Construct a truth table for the conditional statement for a symbolic statement. If the truth table, the last column has all values true, then the conditional statement is a tautology and the argument is valid, else the conditional statement is not a tautology and the argument is not valid. Hence, the tautology conditional statement has a valid argument and not tautology statement has an invalid argument.