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• Not (E): Mismatched tires would only cause loss of control during sudden braking; no
evidence of this was available.
• Not (K): Delation of the left rear tire would have caused a pull to the left, which was not
observed.
Also, if the tire blew out, this would make the effect of mismatched tires insignificant, further
strengthening the probability of not (E). The deflation of the left rear tire could have been an effect
of the car spinning around after impact.
The objective now is to synthesize a Boolean expression for the accident in terms of each con-
tributing factor. First consider the hazard caused by the weather (
W
), where
W
=
A
+
B
A second hazard could have been caused by the roadway (
R
), where
R
=
C
+
D
A third hazard could have been caused by the vehicle (
V
), where
V
=
E
+
K
A fourth factor will be charged to shortcomings of the driver. These could be in terms of errors in
judgment, illness, or intentional violation of the law. Calling this factor
P
,
P
=
I
+
J
Finally, there are factors that did not cause the accident but did add to the severity. Calling these
severity factors
S
,
S
=
F
+
G
+
H
+
L
In the absence of other evidence, it will be assumed that the concurrence of events
W
,
R
,
V
,
P
,
and
S
led to the particular accident. Thus, letting
X
be the occurrence of an accident of this type
and severity,
X
=
WRVPS
= (
A
+
B
)(
C
+
D
)(
E
+
K
)(
I
+
J
)(
F
+
G
+
H
+
L
)
Note:
This Boolean expression is in its simplest form and would be best left as a product of sums.
Before leaving this example, consider the reduction that would result if only the presence of an
accident was considered, and not total event occurrence
X
. Letting
Y
be the accident only,
Y
=
WRVP
Most importantly, those who are to perform modifications on the roadway, vehicles, or drivers might
restrict their considerations to those pertinent subexpressions.
REFERENCES AND RECOMMENDED READING
Boole, G. (1854/2003).
An Investigation of the Laws of Thought
. Prometheus Books, New York.
Boole, G. (1847/1951).
The Mathematical Analysis of Logic
. Basil Blackwell, Oxford, U.K.
Boole, G. (1952).
Studies in Logic and Probability
. Open Court Publishing, LaSalle, IL.
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