Math 430: Homework 8
due: Wednesday, 10/31
Exercises: Chapter 2.2
Problem 11
The structure is (N; +, ). There are many possible answers for the questions below.
(a)
(b)
(c)
(d)
(x) denes 0, where (x) =seq x + x = x
(x) denes 1, where (x) =seq y x y = y
(
Math 430: Homework 7
due: Wednesday, 10/17
1. Fix L = cfw_P for P a binary predicate symbol (i.e. (P ) = 2.)
(1) Write down an L-sentence that is satised in a structure M just in case any point in M is
P M -related to at least two points.
solution: xy z
Math 430: Homework 6
due: Wednesday, 10/10
(This erroneously used to say HW 4)
(1) Fix a language L = cfw_p, f, c where p is a binary function symbol, f is a unary function
symbol, and c is a constant symbol. Let A be the following L-structure:
|A| = N
pA
Math 430: Homework 5
due: Wednesday, 10/3
Exercises: Chapter 2.1
Problem 3.
x a x x b x, or
/
/
x a x x b x
Problem 5.
(a) x(P x y (T y F xy )
(b) y (P y x(T x F yx)
(c) y (P y x(T x F yx), or
y x(P y T x F yx), or
y x(P y T x F yx)
Problem 6.
(a) x(Jx Da
Math 430: Homework 4
due: Wednesday, 9/26
Problem 5.
We will use that (S R) (S R) is a tautology (veriable by truth-table.) We give
a deduction of P from = cfw_S R, R P, S ,
1 , 2 , 3 , 4 , 5 , 6 , 7
explicitly justifying all steps (this is not necessary;
Math 430: Homework 3
due: Wednesday, 9/19
Exercises: Chapter 1.2 Problems 2, 6, 8.
2. (a) Suppose, for contradiction, that there exists a t.a. that makes (P Q)
P ) P false. Then assigns (P Q) P ) to be T and P to be F . In order
for (P Q) P ) to be T und
Math 430: Homework 2
due: Friday, 9/14
Exercises: Chapter 1.2
1 In order to show that it suces to nd one truth assignment that satises
and does not satisfy . Let := (A (B C ) and := (A (B C ) (A
(B C ). Notice that we can make false under any t.a. that
Math 430: Midterm review
Wednesday, 2/29
Sentential logic (3 questions)
(1) (Induction Principle) cfw_ is not complete because for all formulas L0 (cfw_),
1
1
B = BA1 . To show this, prove the following using the Induction Principle on
1
L0 (cfw_): For al