CS103
HO#5
Equivalences
March 31, 2010
1
9 written problem sets, counted equally
Due in class
3 free late days (max. 1 on any assignment)
Not accepted
more than one
class period
late!
Late without a late day: 10%
You may work with others in the class, but you
must write up your problem sets
individually
Revealing an answer denies the other person
the opportunity for the "Aha!" experience
Homework Policy
pq
?
T
T
T
F
F
T
F
F
How many binary logical operators can there be?
p q
p ? q
T T
T
T F
F
F T
T
F F
T
p q
p ? q
T T
T
T F
F
F T
T
F F
T
Observation 1:
The ? connective is pretty weak.
Knowing that
p ? q
is
true only eliminates one possible combination of
p
and
q
.
Observation 2:
If we know
p ? q
is true and we also know
p
is false,
then we have no information about the truth of
q
.
Observation 3:
If we know
p ? q
is true and we also know
p
is true,
then we are sure
q
is true.
The Conditional operator
p q
p
→
q
¬
p
∨
q
T T
T
T
T F
F
F
F T
T
T
F F
T
T
p
→
q
≡
¬
p
∨
q
p q
p
→
q
¬
p
∨
q
T T
T
T
T F
F
F
F T
T
T
F F
T
T
→
is called the
material conditional
, meaning that it is
truthfunctional
The Conditional operator
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HO#5
Equivalences
March 31, 2010
2
p q
p
→
q
¬
p
∨
q
T T
T
T
T F
F
F
F T
T
T
F F
T
T
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 Fall '09
 Logic, ........., Logical connective

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