CSCI 235 HW 1
Section 1.1
1.
Determine which of the following are propositions and their truth
values:
a)
February has 28 days.  True
2.
Let p and q be the propositions
p : I am free today.
q : I go to the gym.
Write these propositions using P and q and
Apropositionisadeclarativesentencethatiseithertrueorfalse.
Examplesofpropositions:
a) TheMoonismadeofgreencheese.
b) TrentonisthecapitalofNewJersey.
c) TorontoisthecapitalofCanada.
d) 1+0=1
e) 0+0=2
Examplesthatarenotpropositions.
a) Sitdown!
b) Whatti
Truth Tables For Compound Propositions
Construction of a truth table:
Rows
Need a row for every possible combination of values for the atomic
propositions.
Columns
Need a column for the compound proposition (usually at far right)
Need a column for t
Disjunction
Thedisjunctionofpropositionspandqisdenotedbypqandhasthistruth
table:
p
q
pq
T
T
T
T
F
T
F
T
T
F
F
F
Example:IfpdenotesIamathome.andqdenotesItisraining.thenpq
denotesIamathomeoritisraining.
TheConnectiveOrinEnglish
InEnglishorhastwodistinctmean
CSCI 235 HW 2
Section1.3
1.
Determinewhetherthefollowingpropositionssatisfytherequirementfor
beingatautology:
a) (pq)p
p q

T
T

T
F

F
T

F
F

p qp
( )
T TT
F TT
F TF
F TF
YESthisisatautology.
b) (pq)q p
p
q
p
q
T
T
FF
T
F
F
F
T
TF
F
F
TT


T
CSCI 235 HW 4
Section 1.5
1.
Translate these statements into English, where the domain for each
variable consists of all real numbers.
a) xy(x < y)
For all cases of number x and some cases of number y,
number x is greater than number y.
b) xyz (x y = z)
F
CSCI235HW3
1.
Letp(x)denote2x+1>8,andUbethedomainofintegers.Findthetruth
valuesforthefollowing:
F
F
F
T
a)
b)
c)
d)
P(0)
P(1)
P(3)
P(4)
a)
b)
c)
d)
e)
2.
LetpropositionalfunctionQ(x,y)denote2x+y=3z,andU(forallthree
variables)containintegers.Findthetruthva
CSCI 235 HW 5
Section 1.6
1. Using Rules of Inference, show that the hypotheses If you buy me a
ticket, then I will go to the ball game, If you do not buy me a ticket, then I will
go to the park, and If I go to park, then I will read a book lead to the
co