Math 2971W-10
INTRODUCTION TO MATHEMATICAL REASONING
Spring 2015
CRN: 43504
HOMEWORK I DUE Wednesday, January 21, at the beginning of the lecture;
resubmission due the Friday of the following week
1. For each of the four mathematical statements below writ
Math 2971W
INTRODUCTION TO MATHEMATICAL REASONING
Fall 2015
CRN: 63345
HOMEWORK VII DUE Tuesday, November 3, at the beginning of the lecture;
resubmission due the Thursday of the following week
1. Prove the following by induction:
7 points
(a) n N (8 | (5
INTRODUCTION TO MATHEMATICAL REASONING
Math 2971W Fall 2015 CRN: 63345
QUIZ 3 NAME:
1. Consider the relation < dened on ?(Z) by: X -< Y E V2161: e X > 33; (y E Y /\ a: < y).
For each of the pairs of sets A, B dened below, determine Whether A 4 B, or B 4 A
INTRODUCTION TO MATHEMATICAL REASONING
Math 2971W Fall 2015 . CRN: 63345
QUIZ 6 NAME:
1. Depict an FL proofskeleton in the vocabulary cfw_+, 0 for the negation of:
V11:(.'z:90 -> El!y(z;y A$+y=0)
Remember that 3! means there is exactly one. 9 points
Nag/0
INTRODUCTION TO MATHEMATICAL REASONING
Math 2971W Fall 2015 CRN: 63345
QUIZ 8 NAME:
1. I_)epict the iactz'on-table for the interpretation (cfw_0,12, f ) of the vocabulary cfw_f (, ) with
f dened by f(a, b), (c, d) = (d ~ a)2, (c b)2) 5 points
(0,0) (0,13
INTRODUCTION TO MATHEMATICAL REASONING
Math 2971W Fall 2015 CRN: 63345
QUIZ 1 NAME:
Translate the following mathematical statements into FL sentences in the vocabulary cfw_<:
1. The intersection of any two sets is a. subset of their difference.
a Vxebma
Math 2971W
INTRODUCTION TO MATHEMATICAL REASONING
Fall 2015
CRN: 63345
HOMEWORK X DUE Thursday, December 3, at the beginning of the lecture;
with no resubmission
1. (a) Depict all 16 binary relations on the set cfw_a, b, numbering them Ri , , R16 , and de
INTRODUCTION TO MATHEMATICAL REASONING
Math 2971W Fall 2015 CRN: 63345
QUIZ 4 NAME:
1. Depict a proof-skeleton for 3223; (m [y /\ V2 (:1; I z > y 12) 6 points
Translate each a | b into 3c (1 - c = b).
oat/ne. aLa-H,
preach, Tkat aLeLL:
W
32%? ww-
cfw_Kare
Math 2971W
INTRODUCTION TO MATHEMATICAL REASONING
Fall 2015
MIDTERM EXAM
CRN: 63345
There are 3 questions worth 70 points altogether, with 60 points being a perfect score;
you may do all or any (parts of ) problems.
1. Write F L sentences in the vocabular
INTRODUCTION TO MATHEMATICAL REASONING
Math 2971W Fall 2015 CRN: 63345
QUIZ 1 NAME:
1. For X = cfw_1, 2 and Y = cfw_2, 3 determine the following sets:
CD (a)XxY(YX)><(XY)
:cfw_(1,2.\(1,3\,(A,a.\,(z,33~ cfw_(3,05
= cfw_(1,23,(1,33,(2,23, (2,3),
03) 730) -
INTRODUCTION TO MATHEMATICAL REASONING
Math 2971W-10
PRACTICE FINAL EXAM
There are 7 problems worth 70 points altogether, with 60 being a perfect score; you
may do all or any (parts of ) problems.
1. (a) For each of the following statements, write an FL s
Math 2971W
INTRODUCTION TO MATHEMATICAL REASONING
Fall 2015
FINAL EXAM
CRN: 63345
There are 10 problems worth 70 points altogether, with 60 being a perfect score.
In the vocabulary cfw_R(, ):
1. Without using any abbreviations write FL sentences in the vo
Math 2971W
INTRODUCTION TO MATHEMATICAL REASONING
Fall 2015
CRN: 63345
HOMEWORK IX DUE Tuesday, November 17, at the beginning of the lecture;
resubmission due the Tuesday of the following week
1. Prove in careful detail: xy Z (x2 = y 2 (mod 6) (x = y (mod
Math 2971W-10
INTRODUCTION TO MATHEMATICAL REASONING
Spring 2015
CRN: 43504
HOMEWORK VI DUE Wednesday, March 18; resubmission due the Friday of the
following week
1. Depict proof skeletons for the following (in the general universe U ):
(a) X = N Y = X (X
Math 2971W-10
INTRODUCTION TO MATHEMATICAL REASONING
Spring 2015
CRN: 43504
HOMEWORK III DUE Wednesday, February 4, at the beginning of the lecture;
resubmission due the Friday of the following week
1. For any two of the following three statements, prove
Math 2971W-10
INTRODUCTION TO MATHEMATICAL REASONING
Spring 2015
CRN: 43504
HOMEWORK VII
DUE Wednesday, March 25 AT THE BEGINNING OF THE LECTURE;
resubmission due the Friday of the following week
1. For T1 , T2 , T3 , defined by
! T1 = 1, T2 = 3,"T3 = 6,
Math 2971W-10
INTRODUCTION TO MATHEMATICAL REASONING
Spring 2015
CRN: 43504
HOMEWORK IV DUE Wednesday, February 11, at the beginning of the lecture;
resubmission due the Friday of the following week
1. Negate the following, leaving your negations as F L s
Math 2971W-10
INTRODUCTION TO MATHEMATICAL REASONING
Spring 2015
CRN: 43504
HOMEWORK VIII
DUE Wednesday, April 1 AT THE BEGINNING OF THE LECTURE (no joke!);
resubmission due the Friday of the following week
1. Consider the function f : R R defined by f (x
Math 2971W-10
INTRODUCTION TO MATHEMATICAL REASONING
Spring 2015
CRN: 43504
HOMEWORK II DUE Wednesday, January 28, at the beginning of the lecture;
resubmission due the Friday of the following week
1. Write, for each of the mathematical statements below,
Math 2971W-10
INTRODUCTION TO MATHEMATICAL REASONING
Spring 2015
CRN: 43504
HOMEWORK X: DUE Wednesday, April 15 at the beginning of the lecture;
resubmission due the Wednesday of the following week
1. Write down all 16 binary relations Ri , , R16 on cfw_a
Math 2971W-10
INTRODUCTION TO MATHEMATICAL REASONING
Spring 2015
CRN: 43504
HOMEWORK IX: DUE Wednesday, April 8 at the beginning of the lecture;
resubmission due the Friday of the following week
1. Determine whether the relations defined below are surject
Math 2971W
INTRODUCTION TO MATHEMATICAL REASONING
Fall 2015
CRN: 63345
HOMEWORK VIII DUE Tuesday, November 10, at the beginning of the lecture;
resubmission due the Thursday of the following week
1. Prove by induction that, for all n N, the Fibonacci numb
Math 2971W
INTRODUCTION TO MATHEMATICAL REASONING
Fall 2015
CRN: 63345
HOMEWORK VI DUE Tuesday, October 13, at the beginning of the lecture;
resubmission due the Thursday of the following week
1. Write F L proof-skeletons for the negations of the followin
INTRODUCTION TO MATHEMATICAL REASONING
Math 2971W Fall 2015 CRN: 63345
QUIZ 10 NAME:
1. Determine which of the following interpretations of the vocabulary cfw_R(, ) satisfy
991: R is symmetric
902: R is antisymmetric 8 points
and provide brief but clear a