Some Additional Practice Proofs

(To save the exercises to your disk you may need to right click on each link and choose 'Save As')

Proofs in which you are NOT allowed to use Taut Con (generally easier)
Exercise: 8.54, 8.58, 8.59,8.60

Proofs in which you ARE allowed to use Taut Con, citing at most two sentences. (generally harder)
Exercise: 8.55, 8.56, 8.57

Note: In the proofs where you are allowed to use Taut Con, you will most often use it for the following two patterns of inference:

Disjunctive Syllogism

A v  B                    A v B
~ A                        ~ B
B                            A

Modus Tollens

A -> B
~ B
~ A