CS103A
HO#15
SlidesConditionals
1/28/08
1
Conditionals
P Q
P ? Q
T T
T
T F
F
F T
T
F F
T
Conditionals
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.
Conditionals
P Q
P ? Q
¬P
∨
Q
T T
T
T
T F
F
F
F T
T
T
F F
T
T
Conditionals
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
Conditionals
P Q
P
→
Q ¬P
∨
Q
T T
T
T
T F
F
F
F T
T
T
F F
T
T
The best rendering of
P
→
Q
in English is "
if P, then Q
"
Antecedent
Consequent
P Q
P
→
Q ¬P
∨
Q
T T
T
T
T F
F
F
F T
T
T
F F
T
T
$40K
New Copier
$40K
→
New Copier
Is this true:
If the department gets an extra $40K, we'll buy a new copier.
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View Full DocumentCS103A
HO#15
SlidesConditionals
1/28/08
2
P Q
P
→
Q ¬P
∨
Q
T T
T
T
T F
F
F
F T
T
T
F F
T
T
If the moon is not made of cheese, then triangles have three sides.
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 Winter '07
 Plummer,R
 Computer Science, Logic, Modus ponens, Modus tollens, 40k, ¬P, new copier

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