Geoffrey J Grimaud ITCS 2175-051 Page 1
[AZL994]
Define the following propositions:
p: I will return to college.
q: I will not get a job.
Translate the following English sentence into logical expressions u
ITCS2175PetarKanev
Section3.13.7Exercises
Setsandsubsets
1.
2.
SetsA,C,andFaredefinedasfollows:
A=cfw_x
Z
:xisanintegermultipleof3
C=cfw_4,5,9,10
F=cfw_4,9,16
Indicatewhichstatementsare
True
,andwhichare
False
:
a. FC
FALSE
b. FC
FALSE
c. 144A
TRUE
d. 15A
Geoffrey J Grimaud ITCS 2175 Section 1.2
Define the following propositions:
p: The weather is bad.
q: The trip is cancelled.
r: The trip is delayed.
Translate the following English sentence into logical expressions using the definitions above:
a)
b)
c)
d)
ITCS2175PetarKanev
Section2.12.5Exercises
Homework Problems: Exercises Sections 2.1-2.5
1.
Findacounterexampleforeachofthestatementsbelow:
a. Everymonthoftheyearhas30or31days.
Februaryhas28days
b. If n isanintegerand n2 isdivisibleby4,then n isdivisibleby
ITCS2175PetarKanev
Section4.14.6Exercises
1. Consider the following function from
. List the elements in its domain, target, and
f (x) = x2
range.
Domain:
(1,2,3,4,5,.)
Target:
(1,4,9,16,25.)
Range:
cfw_y:(x,y)f,forsomexX
2. Considerthefollowingfunction
ITCS2175PetarKanev
Section1.81.12Exercises
Homeworkproblems:Nestedquantifiers(1.81.9)
1) Determinethetruthvalueofeachexpressionbelowifthedomainisthesetofallrealnumbers.
a)
b)
c)
d)
(Iftrue,giveanexample.)
TRUE,x=0&y=20
xy(xy=0)
(Iffalse,giveacounterexampl
Determine whether each of these conditional statements is true or
false.a) If
6+1=6
, then unicorns exist.
True because the first statement is true and the second statement is
false.
True because both statements are false.
False because the first statemen
ITSC 2175, Logic and Algorithms, Fall 2016
Problem Set#5 Solution
1. Define the following propositions:
p: He studied for the test.
q: He failed the test.
Use a truth table to prove the following argument. The hypotheses are:
He studied for the test or
