Module 7.edited
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Module 7: Propositional Logic
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Module 7: Propositional Logic
Conversation:
John:
Hey, I heard that smoking is bad for your health.
Sarah:
Well, yes, that is true. Smoking is known to cause various health problems.
John:
But my grandfather smoked all his life, and he lived to be 90.
Sarah:
That is true, but it is not guaranteed that smoking will not harm you. Some people are
lucky and do not experience serious health issues despite smoking.
John:
I read an article that said smoking in moderation might even have some health benefits.
Summary and Analysis:
The subject of smoking and its potential adverse health effects is mentioned in the
conversation between John and Sarah that is being described. The logical linkages between the
symbolic logical claims in this discussion can be determined by breaking them down into truth
tables.
The claim made in Statement 1 (S) is that "Smoking is bad for your health." This claim is
categorized as dependent, meaning it is not a universal reality. Individual conditions and health
results, which can differ from person to person, affect the truth value of S. As a result, it is
neither an always true tautology nor an always false self-contradiction (Hurley, 2014).
Different viewpoints on smoking are introduced in statements 2 (P) and 3 (Q). According
to statement 2, "Some people who smoke live long lives," smoking does not always result in
health problems or shorter lifespans. A different perspective is presented in Statement 3,
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"Smoking in moderation might have health benefits," which contends that controlled or moderate
smoking might potentially provide some health benefits.
It is clear from comparing P and Q that they are not logically equivalent. Logically
comparable statements would always have the same truth value, but that is not the case in this
instance. P and Q are not in contradiction with one another, but they can both be true in some
circumstances, proving that they are not. This illustrates how smoking may have various effects
on different people, with some people having long lives (P) and others enjoying health benefits
from moderation (Q). 2022) (Mohammad Ghorbanian).
The overall argument presented by these statements, labeled as "S (P Q)," is now
determined to be true. Because the conclusion, denoted by "P Q" (both P and Q are valid),
logically follows from the premises, denoted by "S" (Smoking is hazardous for your health), the
argument is valid. Whether S is proper or incorrect, this argument remains valid under all
imaginable circumstances.
Setting up an Argument:
Argument: S → (P
∧
Q)
Construct a truth table for this argument to determine its validity:
S
P
Q
P
∧
Q
S → (P
∧
Q)
T
T
T
T
T
T
T
F
F
F
T
F
T
F
F
T
F
F
F
F
F
T
T
T
T
F
T
F
F
T
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4
S
P
Q
P
∧
Q
S → (P
∧
Q)
F
F
T
F
T
F
F
F
F
T
The discussion between John and Sarah demonstrates the complexity of the issue of
smoking and its adverse impacts on health. We have established that Statement 1 (S) is
contingent, Statements 2 (P) and 3 (Q) are not logically equivalent but also not contradictory, and
the argument as a whole is valid due to the consistency between the premises and the conclusion
by translating the statements into symbolic logic and using truth tables. This investigation
demonstrates the value of using logic to assess arguments, even in commonplace conversations
(Howat et al., 2022
)
.
Conclusion
The validity of the argument "S (P Q)" is established by the consistency of its premises
and conclusion, and as a result, the argument is valid. The idea that the conclusion must likewise
be proper if the premises are valid is the foundation of logical reasoning. Whether the premises
(S, P, and Q) are true or untrue, the argument in this instance is valid under any possible scenario.
It is determined that Statement 1 (S), the first premise, is dependent. This implies that it is
only sometimes accurate or incorrect in every situation. Instead, its validity or untruth is
dependent upon a particular set of circumstances.
When compared, it is discovered that statements 2 (P) and 3 (Q) are neither logically
equivalent nor incompatible. According to Wolf, Schwerhoff, and Müller (2023), contradictory
assertions always have opposite truth values, but logically comparable statements always have
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the same truth value. The fact that P and Q may both coexist as accurately in this context,
proving they are not mutually exclusive and that they do not always have the same truth value,
proving they are not logically comparable, shows that they are not incompatible.
The argument's continued validity may be inferred from the fact that the conclusion
consistently agrees with the premises. This emphasizes the value of logic in evaluating the
viability of arguments since it enables us to determine the veracity and soundness of claims even
in casual interactions when arguments may not always be expressed symbolically.
References
Howat, A., Bruschke, J., & Ocampo, M. (2022). Critical thinking instruction for the post-truth
era.
Argumentation and Advocacy
, 1-19.
Hurley, P. J. (2014).
A concise introduction to logic
. Cengage Learning.
Mohammad Ghorbanian, H. (2022). A Study of the Fallacy of Begging the Question and Its
Argumentative Structure.
Naqd Va Nazar
,
27
(108), 147-172.
Wolf, F. A., Schwerhoff, M., & Müller, P. (2023). Concise outlines for a complex logic: a proof
outline checker for TaDA.
Formal Methods in System Design
, 1-27.