Question

You don't need to construct a Venn Diagram, it is just part of the instruction. Just determine whether or not the argument is valid or not with support.
Construct a Venn diagram to determine the validity of the given argument.
Argument:
1. All poets are loners.
2. All loners are taxi drivers.
Therefore, all poets are taxi drivers.

Choices:
- The argument is valid.
- The argument is invalid.

Please provide explanation for whether the argument is valid or not.

Answer 1

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.