I.
Proofs in Statement Logic:
a.
Ex:
i.
(A.B)
ii.
(B>(C v D))
iii. ~D
iv.
:. C
v.
It can be deduced from (A.B)’s truth that B is true.
vi.
This means that the antecedent of the second premise is true, and thus
the consequent must also be true for the conditional to be true.
vii.If the consequent is true, C and D cannot be both false.
1.
Furthermore, noting that B > (C v D), and B is true, (C v D) must
be true because this is an instance of Modus Ponens.
viii.
Now, given that (C v D) MUST be true, and given that ~D is
true and thus D is false, it follows that C MUST be true, via the
disjunctive syllogism argument form.
1.
Thus, the argument is valid.
b.
(p.q) :. q = “simplification” valid form
c.
In proofs, valid forms are referred to as inference rules, and are means of
deducing steps in a proof.
d.
Inference rules:
i.
Modus Ponens
ii.
Modus Tollens
iii. Disjunctive Syllogism
1.
p v q, ~p, :. q
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
iv.
Hypothetical Syllogism
1.
p>q, q>r, :. p>r
v.
Constructive Dilemma
1.
p v q, p>r, q>s, :. r v s
vi. simplification
1.
p.q, :. p
vii.Conjunction:
1.
p, q, :. p.q
viii.
Addition:
1.
p, :. p v q
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 peterhodges
 Logic, inference rules, Rue

Click to edit the document details