Transcript Slide 1

No new reading for Monday. Exam #2 is
Wednesday.
My office hours on Monday are cancelled. I’ll
be out of town.
Exam #2: Outline
-Use a truth-table to categorize a single
statement (as a tautology, contradiction, or
contingent statement)
-Truth-table test for validity (method of
exhaustive search)
-Constructing an interpretation to test for validity
-Proof of a theorem
-Proof of an argument
~Elimination
a1,…,an
(j) ~q
.
.
b1,…,bn
(k) q
.
.
a1,…,an, b1,…,bn (m) ∧
j > k or j < k
j, k ~E
~Introduction
j
(j) p
.
.
a1,…,an
(k) ∧
.
.
{a1,…,an}/j (m) ~ p
j > k, j < k, or j = k
Assumption
j, k ~I
DN (Double Negation)
a1,…,an (j) ~~p
.
.
a1,…,an (k) p
j, DN
This rule is needed when you use ~I to derive
something “positive” (i.e., something that
does not have a tilde as its main connective).
Assume the negation of your goal. Use ~I to
get two adjacent tildes. Then use DN to
arrive at your target.