Midterm Guidelines
Pay special attention to the main arguments presented in the texts below. It is also
important to remember the names and historical periods discussed in these texts. For
example, you should know who Samuel Parris is, and you should know
Math 512 Test 3
April 17, 2013
Question:
1
2
3
4
5
6
Total
Points:
9
8
13
10
9
4
53
Score:
1. (9 points) The ISBN book numbers have a check digit designed so that a valid ISBN number x1 x2 x10
satises the equation
x1 + 2x2 + 3x3 + + 10x10 = 0 mod 11.
(a)
Math 512 Test 2
March 20, 2013
Question:
1
2
3
4
5
6
Total
Points:
10
10
12
5
7
9
53
Score:
n
1. (10 points) Prove by induction:
2i = n(n + 1)
i=1
2. (10 points) Write an algorithm (or computer program or Turing machine) to check whether a number
n is eve
6. (9 points) Fill in the blanks for the following axiomaticproof in PA.
Theorem 1. l- x+y = y+z
Proof. The proof uses induction on y. Let A(y) denote + 5 +X
1. a: + 0 = m S-
2.m=0+:1: Prop2
3. {KiO =0+7< Prop 1c,1,2
Thus, +- A( ).
1. + = {*K H
Math 512 Test 1
February 13, 2013
1. Determine whether the following are tautologies. (You may use truth tables, standard logical identities,
or informal reasoning.)
(a) A (B C ) (A B ) (A C )
(b) (x) A(x) (y )B (x, y ) (y ) (x)A(x) (x)B (x, y )
2. Simpli
Math 512 Test 1 Review
February 8, 2013
For the test, I will give you the axioms A1 - A10. For the formal proofs (see problem 5 below), you will
only be allowed to use these. On the other problems, you are free to use any of the standard logical identitie
Math 512 Homework 4: Due Feb 27, 2013
February 20, 2013
1. Let < be a relation on a set S that satises the following two properties
Transitivity: If a < b and b < c, then a < c for all a, b, c S .
Trichotomy: For all a, b S , exactly one of the followin
Math 512 Homework 3: Due Feb 13, 2013
February 6, 2013
1. Prove the following theorems directly from the axioms and deduction theorem.
(a) B C, C D B D
(b) B B
(c) (x)(B C) (x)B (x)C)
Propositional Logic
Axioms:
(A1) B (C B)
(A2) (B (C D) (B C) (B D)
(A3)