BICONDITIONAL:ARGUMENT, VALID AND INVALID ARGUMENT

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MTH001 Elementary Mathematics

LECTURE # 5

EXAMPLE

An interesting teacher keeps me awake. I stay awake in Discrete Mathematics class.

Therefore, my Discrete Mathematics teacher is interesting.

Is the above argument valid?

ARGUMENT:

An argument is a list of statements called premises (or assumptions or

hypotheses) followed by a statement called the conclusion.

P1 Premise

P2 Premise

P3 Premise

. . . . .. . . . .

Pn Premise

______________

∴C Conclusion

NOTE The symbol \ read "therefore," is normally placed just before the conclusion.

VALID AND INVALID ARGUMENT:

An argument is valid if the conclusion is true when all the premises are true.

Alternatively, an argument is valid if conjunction of its premises imply conclusion.That is

(P1∧ P2 ∧ P3 ∧ . . . ∧ Pn) → C is a tautology.

An argument is invalid if the conclusion is false when all the premises are true.

Alternatively, an argument is invalid if conjunction of its premises does not imply conclusion.

EXAMPLE:

Show that the following argument form is valid:

p→q

∴ q

SOLUTION

premises

conclusion

p→q

critical row

EXAMPLE

Show that the following argument form is invalid:

p→q

∴ p

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MTH001 Elementary Mathematics

SOLUTION

premises

conclusion

p→q

critical row

EXERCISE:

Use truth table to determine the argument form

p∨q

p → ~q

p→r

∴ r

is valid or invalid.

premises

conclusion

p∨q

p→~q

p→r

critical rows

The argument form is invalid

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