Question

the following is an excerpt from a speech by a reknown plumber.
he or she who is without plumbing skill can work without a wrench. there is no one here who does not have a license in his or her pocket. i know, and i know them by name.
the above argument can be expressed as shown below.
no plumber is one who should work without a wrench.
all people here are plumbers.
therefore, no person here is one who should work without a wrench.
use an euler diagram to determine whether the argument is valid or invalid.
select all possible euler diagrams that best represent the two premises.
a.
plumber
person
work without a wrench
b.
plumber
person
work without a wrench
c.
person
plumber
work without a wrench
d.
plumber
work without a wrench
(person)

Explanation:

• The first premise "No plumber is one who should work without a wrench" means the set of plumbers and the set of those who work without a wrench are disjoint.
• The second premise "All people here are plumbers" means the set of people here is a subset of the set of plumbers.

Looking at the Euler - diagram options:

• Option A: The set of "person" (assuming "person" here refers to "people here") is a subset of "plumber", and "plumber" and "work without a wrench" are disjoint. This correctly represents the two premises.
• Option C: The set of "person" (assuming "person" here refers to "people here") is a subset of "plumber", and "plumber" and "work without a wrench" are disjoint. This also correctly represents the two premises.

Answer:

A.
C.