Question

All who studied commerce enjoy sports. No tax consultant enjoys sports. All those who enjoy sports love classical music. If the above sentences are true, which of the following also must be true?

• A. No one who enjoys classical music is a tax consultant by profession.
• B. Every tax consultant enjoys classical music.
• C. No tax consultant enjoys classical music.
• D. No tax consultant studied commerce.
• E. No one who studied commerce enjoy classical music.

Hint:

- Convert statements to simple implications and chain them.
- To prove “must be true,” look for contradictions when assuming the opposite.
- Beware of options that overextend conclusions (e.g., about classical music without the sports link).

Answer 1

The Correct Option is D

Step 1: Translate the statements into logic.
Let \(C=\) studied commerce, \(S=\) enjoys sports, \(M=\) loves classical music, \(T=\) tax consultant. We have:
\(\quad C \Rightarrow S\) (all commerce students enjoy sports),
\(\quad T \Rightarrow \neg S\) (no tax consultant enjoys sports),
\(\quad S \Rightarrow M\) (all sports lovers love classical music).
Step 2: Derive what must be true.
If someone were both \(T\) and \(C\), then \(C \Rightarrow S\) and \(T \Rightarrow \neg S\) would yield \(S \land \neg S\), a contradiction. Hence \(T \Rightarrow \neg C\). Therefore, no tax consultant studied commerce.
Step 3: Check other options.
(A) Not implied: a tax consultant might love classical music without liking sports.
(B) Cannot be true from premises (nothing says all \(T\) love classical).
(C) Not implied for the same reason as (A).
(E) False: \(C \Rightarrow S \Rightarrow M\), so commerce students do love classical music.
Thus, only (D) must be true.