MATH S104 Lecture 1 Inclass Problem Solutions
June 23, 2009
Problem 1
*
:
Given the following statements
p
,
q
, and
r
, convert English to logical form or
viceversa.
p
: “DATAENDFLAG is o
ff
”
q
: “ERROR equals 0”
r
: “SUM is less than 1000”
a) “DATAENDFLAG is o
ff
, ERROR is 0, and SUM is at least 1000”
p
∧
q
∧
¬
r
b)
(
¬
p
∨
q
)
∧
r
“SUM is less than 1000 and either DATAENDFLAG is on or ERROR equals 0”
c) “Either DATAENDFLAG is on or it is the case that both ERROR equals 0 and SUM
is less than 1000”
¬
p
⊕
(
q
∧
r
)
Problem 2
†
: Generate a logic circuit for the following Boolean expressions.
For each of these problems, there are multiple correct answers.
a)
p
∨
(
¬
p
∧
¬
q
)
OR
AND
NOT
NOT
p
q
b)
(
p
∧
¬
q
)
∨
(
¬
p
∧
r
)
OR
AND
NOT
NOT
q
p
r
AND
1
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c)
p
⊕
q
OR
AND
NOT
p
q
AND
Problem 3
*
: Use De Morgan’s law to negate the following:
a) “John is 6 feet tall and he weighs at least 200 pounds.”
“John is not 6 feet tall or he weights less than 200 pounds.”
b) “The bus was late or Tom’s watch was slow.”
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 Spring '10
 Various
 Logic, Addition, distributive negation, commutative associative negation, commutative negation domination

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