Problem Set 4
1. As stated in problem set 2, A directed graph can be represented as a set N of nodes and a
predicate P( x , y ) where x and y are in the set of nodes. The expression P( x , y )
is read "There is an edge from
x to
y ."
Alternatively, a dire
Sample Final Exam Answers
COMP2300-1 Spring 2015
1. Prove that ! (1)! ! = (1)! ( + 1)/2 whenever n is a positive integer.
!
Proof by mathematical induction. Let P(n) be the assertion that the equation above is
true.
Class 18 Friday, May 22, 2015
Section 1
Mike Goss
Revised
Today's Class
! Problem Set 7 discussion (0-15 min.)
! Problem set 7 collected
! This was the last problem set
! Continue with new material, Sec. 7.3-
Class 16 Friday, May 16, 2015
Section 1
Mike Goss
Today's Class
Problem Set 6 discussion (0-15 min.)
Problem set 6 collected
Problem set 7 assigned
Continue with new material, Sec. 6.1(cont.)-6.4
Review Prob
COMP 2300:
Discrete Structures
Name:
Finals
Points 30%
This exam is closed-book. All questions have equal weight. If a question has multiple parts,
the weight assigned to that question is divided equally among all parts unless specied otherwise. The work
^=and;v=or;Xor;Biconditional:TF-F;ff-t;FT-F;TT-T;
Translate: you can access internet in campus if ur cs major or not fs;
a->(cv nfs);
DeMorganLaw: -(p^q)=-pV-q; -(pVq)=-p^-q; negation law: pV-p=T;p^-p=F; IdentityLAW: p^T=p; pVF=p;
Distribute law: (pV(q^r)
COMP2300 Spring 2015
Problem Set - Week 3
Sec. 1.7
Ex. 16: Prove that if m and n are integers and the product mn is even, then either m
is even or n is even.
Ex. 18: Prove that if n is an integer and 3n+2