Consider the following argument:

"To become an engineer, one must hold a university degree. All musicians are underpaid. Some scientists are musicians. No university graduate is underpaid."

Which one of the following is not a valid conclusion based on the above statements?

(a) Some scientists are not engineers.
(b) Some engineers are not scientists.
(c) Engineers are not underpaid.
(d) Musicians are not engineers.

Question

Consider the following argument:

"To become an engineer, one must hold a university degree. All musicians are underpaid. Some scientists are musicians. No university graduate is underpaid."

Which one of the following is not a valid conclusion based on the above statements?

(a) Some scientists are not engineers.
(b) Some engineers are not scientists.
(c) Engineers are not underpaid.
(d) Musicians are not engineers.

ONLiNE UPSC · Accepted Answer

Let's analyse the premises and how they relate:

Engineers &rarr; University degree

All musicians &rarr; Underpaid

Some scientists &rarr; Musicians

No university graduate &rarr; Underpaid

From (1) and (4): Engineers are university graduates, and no graduate is underpaid &rarr; Engineers are not underpaid &rarr; (c) is valid.

From (2) and (4): Musicians are underpaid, so no musician is a university graduate &rarr; therefore, musicians cannot be engineers &rarr; (d) is valid.

From (3): Some scientists are musicians &rarr; and musicians cannot be engineers &rarr; so some scientists are not engineers &rarr; (a) is valid.

(b) Some engineers are not scientists &mdash; this cannot be concluded because there's no info on the number of engineers who are scientists.

Hence, option b is correct answer.

Deductive Reasoning

Analyzing Arguments

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