Math 2534
Solution to Worksheet 1 on Logic
Sp 2010
1)
Given the following statements below:
P:
May goes hiking
Q:
Moose are on the trail
R:
It is raining
Part A:
Convert the following sentences into symbolic logic form.
a)
May goes hiking and it is raining.
P
Q
∧
b)
May goes hiking but it is not true that moose are on the trail
P
Q
∧
c)
The following statement is not true. Moose are not on the trail but May does
not go hiking.
(
)
Q
P
Q
P
∧
≡
∨
By De Morgan’s Law
d)
It is sunny or May does not go hiking.
(
)
R
P
∨
e)
Either it is raining or Moose are on the trail.
R
Q
⊕
Part B:
Convert the following symbolic logic into a natural conversational English
sentence.
a)
(
)
R
Q
P
∧
∨
It is raining and the moose are on the trail, or May is not hiking.
b)
(
)
P
Q
∧
By DeMorgan’s
law we have:
May is not hiking or Moose are not on the trail
c)
(
)
Q
P
Q
∨
∧
by Absorption law we have:
Moose are on the trail.
3)
Using truth tables, verify the following; (Use a detailed and labeled truth table)
a)
(
)
(
)
(
)
w
s
t
w
s
w
t
∧
∨
=
∧
∨
∧
b)
(
)
w
w
t
w
∧
∨
=
c)
(
)
k
h
k
h
∨
=
∧
a) SEE NEXT PAGE
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(
)
(
)
(
)
w
s
t
s
t
w
s
t
w
s
w
t
w
s
w
t
T
T
T
T
T
T
T
T
T
T
F
T
T
T
F
T
T
F
T
T
T
F
T
T
T
F
F
F
F
F
F
F
F
T
F
T
F
F
F
F
F
F
T
T
F
F
F
F
F
T
T
T
F
F
F
F
F
F
F
F
F
F
F
F
∨
∧
∨
∧
∧
∧
∨
∧
Since column 5 and column 8 have the same truth values we know that
our conjecture is true
and
(
)
(
)
(
)
w
s
t
w
s
w
t
∧
∨
=
∧
∨
∧
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 Spring '07
 MPMcQuain
 Math, Logic, Given name, Raft, Rafting

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