CS 173: Discrete Structures, Spring 2010
Quiz 1 Solutions
Notice that the two sections had slightly different versions of many questions, and this
document contains solutions to all of them.
1. (1 point) Give the day and time when your assigned discussion section meets. State
explicitly if you have switched sections recently.
Solution:
This obviously varies from person to person.
2. (4 points) Simplify or find the values for the following expression:
Solution:
log
k
(
k
2
) = 2 log
k
(
k
) = 2
(log
k
k
)
2
= 1
2
= 1
gcd(42
,
15) = 3
lcm(6
,
21) = 42
3. (4 points) Give a truth table for the following expression and (using your truth table
or other means) find a simpler expression equivalent to it.
Solution:
p
∧
(
p
∨
q
) =
p
(
p
∧
q
)
∨
q
=
q
p
q
p
∨
q
p
∧
(
p
∨
q
)
T
T
T
T
T
F
T
T
F
T
T
F
F
F
F
F
p
q
p
∧
q
(
p
∧
q
)
∨
q
T
T
T
T
T
F
F
F
F
T
F
T
F
F
F
F
1
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4. (4 points) If
∑
n
k
=0
2
k
= 2
n
+1
−
1, give a closedform expression for the following sum
mation. Show your work.
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 Spring '10
 FLECK
 Logic, Equivalence, slightly different versions, following sumk mation, simpler expression equivalent

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