In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusion(s) logically follows/follow from the statements. Statements: All teachers are dancers. All dancers are engineers. Some engineers are beautiful. Conclusions: I. All teachers are beautiful. II. Some dancers are beautiful.

Correct — A.

Rule: a conclusion follows only if it holds in every diagram the statements allow. One counter-arrangement kills it.

The two universals chain: teachers are inside dancers, dancers are inside engineers. The third statement attaches 'beautiful' to part of the engineer circle and never says which part.

So draw the beautiful overlap on the stretch of engineers lying outside dancers. Every statement stays true, yet no dancer and no teacher is beautiful.

That one drawing defeats conclusion I (all teachers are beautiful) and conclusion II (some dancers are beautiful), so neither follows → option (a).

Why the others are wrong

• (b)
  Only conclusion II follows. — Conclusion II needs at least one dancer to be beautiful, but the 'some engineers' overlap is free to sit entirely in the part of engineers that holds no dancer.
• (c)
  Both conclusions I and II follow. — This asks for conclusion I as well, and the statements give 'beautiful' to only part of the engineers — never to all of them, and never to any named subgroup.
• (d)
  Only conclusion I follows. — Conclusion I actually implies II, since every teacher is a dancer. II already fails, so I cannot stand on its own.

Syllogism marking is not about plausibility. A conclusion follows only when it is true in every arrangement consistent with the statements, so the work is to hunt for one arrangement that breaks it.

Two universals in a chain do give a genuine conclusion: all teachers are dancers and all dancers are engineers yields all teachers are engineers.

But a particular premise combined with universals cannot produce a definite particular conclusion about the inner circles. 'Some engineers are beautiful' leaves the overlap free to move, and moving it is enough to break both conclusions.

Key facts

• All teachers are dancers and all dancers are engineers together give 'all teachers are engineers'.
• A particular statement does not say which members it covers, so its overlap can be placed outside any inner circle.
• A conclusion fails as soon as one consistent diagram contradicts it.

Common traps

• Reading 'some engineers are beautiful' as though the beautiful engineers were the dancer-engineers
• Accepting conclusion II because dancers are engineers, which fixes the direction of the chain but not of the overlap

No directly related past PYQ was found.