Consider the following statements Statement 2: All ministers must be politicians.

Question

Consider the following statements:

Statement 1: All graduates are teachers.

Statement 2: All ministers must be politicians.

Statement 3: No politician is a graduate.

Which of the following conclusions can be logically drawn from the above statements?

1. A. Some teachers are graduates. (Correct answer)
2. B. All teachers are loyal.
3. C. Some teachers are ministers.
4. D. No conclusion can be drawn.

Correct Answer

Option A — Some teachers are graduates.

Detailed Solution & Explanation

The correct answer is Some teachers are graduates..

Key Points

• From *All graduates are teachers*, the class of graduates lies wholly inside the class of teachers.
• Converting a universal affirmative gives a particular statement: if all graduates are teachers, then some teachers are graduates.
• This conversion is valid provided the subject class is non-empty, which syllogistic convention assumes.

Additional Information

• Option B introduces *loyal*, a term found nowhere in the premises. A conclusion may never contain a new term.
• Option C cannot follow: ministers are politicians, and *no politician is a graduate*, so ministers are excluded from graduates — nothing links ministers to teachers.
• Option D is wrong because a valid conclusion does exist.
• Remember the conversion rules: *All A are B* converts only to *Some B are A*; *No A is B* converts fully to *No B is A*.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*