Arguments

Arguments in Discrete Mathematics

–        An argument is a sequence of statements. All statements except the final one are called premises (or assumptions or hypotheses). The final statement is called the conclusion.

–        An argument is considered valid if from the truth of all premises, the conclusion must also be true.

–        The conclusion is said to be inferred or deduced from the truth of the premises

–        Test to determine the validity of the argument:

•          Identify the premises and conclusion of the argument

•          Construct the truth table for all premises and the conclusion

•          Find critical rows in which all the premises are true

•          If the conclusion is true in all critical rows then the argument is valid, otherwise it is invalid

–        Example of valid argument form:

•          Premises: p Ú (q Ú r) and ~r, conclusion: p Ú q

–        Example of invalid argument form:

•          Premises: p à q Ú ~r and q à p Ù r, conclusion: p à r