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Answer:
It is valid.
Venn Diagram is attached.
I also provided a truth table.
I also provided a couple of names this argument could be called.
Please let me know if you have any questions about this question.
Thank you kindly.
Step-by-step explanation:
If a person is a poet, then that person is a loner.
If a person is a loner, then that person is a taxi driver.
If a person is a poet, then that person is a taxi drive.
This is in the form:
p->q
q->r
Therefore, p->r.
This is an example of a hypothetical syllogism.
The first thing my mind goes to when seeing this is the transitive property which says if A is related to B and B is related to C then A is related to C.
So this syllogism also has another name and it is called the principle of transitivity of implication.
Let p=person is a poet, q=person is a loner, and r=person is a taxi driver.
I'm going to make a truth table and compare the truth values of the propositions to the conclusion.
Since we have 3 variables, we are going to need 2^3=8 rows.
p q r p->q q->r (p->q) and (q->r) conclusion=(p->r)
T T T T T T T
T T F T F F F
T F T F T F T
T F F F T F F
F F F T T T T
F F T T T T T
F T F T F F T
F T T T T T T
So we are trying to see if we ever have the preposition part true and the conclusion false.
That doesn't happen so the argument is valid.
