39 L iii10M
Let X , Y, and Z be sets. Below is an outline of a proof of the claim
(XUYUZ)=Yn?r17
by proving
NI
(XUYUZ)Yn-?n A Yn'TFnZgXUYUZ)
For your proof, use only the denitions of n, U, \, (El, and the prepositional
equivalences in Table 6.
a)P
EEK/IESoLuTzotx/s
Let P(n) be the following statement:
2) What is the inductive hypothesis? Pk)
POO (Jennies _.>E;m:(5vpz ;
a: l
3) What do you need to prove in the inductive step? F0?) '3 F(k+_l) cfw_11" F3" )
POM-l) dmh 351-:Q<+1)!_I
3) Complete the ind
WSQLU TI OMS
For the following identify whether the formula denes a. function. If it is a.
function, identify Whether it is onetoone, onto, neither, or both (no proof
K
is required):
1)
f1.Z)Z
f1($)=|37|
2)
f2 :N>Z
13(3): lml
f2 .Z>N
f2(-L') 2 I33!
,- 4)
Quiz 9
NAME: SOLUTION
Write down the first 5 elements of the sequence cfw_an , where n = 0, 1, 2, 3, 4, 5, . . .
In addition, give a recursive definition for an . Do not forget the base case.
(You do not need to prove it is correct).
1) an = n + 10
a) Fir
313% 90th 10 NS
1. Master Method
Use the master theorem to prove the following claims. Justify
your answers.
T(n:) $(nK3)+1:
We? .~_
T(n)=16T(n/4)+n2
oleyt-Uf
(M W
COS/L 2- 10:)
m).
Ht) 9 (2)
W G <9le
To) 6 E) (193)
ssSOLUTEQNS
There is a person who has seen every movie.
Let P be the set of all people.
Let M be the set of all movies.
Let S (as, 3;) denote x has seen y.
1. Write a nested quantier to express this English sentence.
2. Write the negation of this nested q
CS 2073-002 Computer Programming
with Engineering Applications
Fall 2009
Instructor Dr. Turgay Korkmaz
Homework Test
Due by Friday, Sept 11, 2009, 5pm
! NO LATE HOMEWORK WILL BE ACCEPTED !
Total 00 points
HW Question:
This is just a test! I just want to m
iii: 5 9 Lil Ti 0 l\/ 3
Use the loop invariant (I) to show that the code below correctly
computes 100m. First use induction to show that (I) is indeed a
loop invariant, and then draw conclusions for theatelmination of 70/ W
the while loop. k Lswdr \cfw_\