MTH 302A Handout:
Classical Propositional Sequent Calculus (SC) and
Semantic Tableaux
March 2, 2016
1
The Syntax
The alphabet is the same as in P C, viz.
1.1
The Alphabet
(a) A countable set PV of Propositional Variables (or letters) p1 , p2 , .
(b) Logic

First Order Logic - Handout and Assignment I
1
1.1
The syntax
The alphabet
(a) A countable (non-empty) set V of variables x1 , x2 , .
(b) A countable (non-empty) set of predicate symbols pn1 , pn2 , ., for any
n( N), where n denotes the arity of the predi

Assignment II
January 14, 2016
Q1. Suppose we assign the following truth function to the conditional :
t1
T
T
F
F
t2
T
F
T
F
t1 t2
T
F
T
F
Show that with this truth function for , the argument form p q q p is
invalid.
Q2. Show that there is a bijection be

Assignment 3
February 1, 2016
Definition 1. A set C of connectives is adequate if for every n 1 and every n-ary
truth function f , there is a wff with propositional variables p1 , p2 , . . . , pn such that (1)
f = f ; (2) the connectives that occur in are

MTH 302(A)
First-order theories
April 11, 2016
1
Some consequences of the deduction procedure
of FOL
Recall the axiomatization for FOL.
Axioms:
A1 ( ).
A2 ( ( ) ( ) ( ).
A3 ( ) ( ).
A4 x( ) (x x).
A5 x (t/x), if t is free for x in .
A6 x, if x is not free

MTH 302(A) Handout:
Boolean algebras
1
Some properties of the logical connectives
Let us choose and fix any tautology in the set F of all wffs of PC (over some
set P V of propositional variables) and denote it by >. So for every tautology
, we have >. Sim

Assignment I
January 7, 2016
Q1. Let v be the truth assignment such that v(p1 ) = T , v(p2 ) = F , v(p3 ) = F . Find
v(p1 (p2 p3 ).
Q2. Let A be the wff (p1 p2 ) p1 ) p2 . Find a truth assignment that satisfies
A and one that does not.
Q3. These puzzles a

Assignment 5
February 12, 2016
Theorem 1. (Soundness) If cfw_1 , 2 , . . . , n ` , then the argument form 1 , 2 , . . . n
is valid, i.e. cfw_1 , 2 , . . . , n |= .
Q1. Use the above theorem to show that the following argument forms are valid:
1. , , ,