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 conclusions logically follows/follow from the statements. Statements: All red are green. All green are pink. No pink is blue. Conclusions: I. No green is blue. II. Some blue are red.

Correct — B. Chain the two 'all' statements, then bring in the negative.

Rule: red sits inside green, green sits inside pink, and pink and blue do not touch.

Conclusion I: every green is inside pink, and no pink is blue, so no green is blue. It follows.

Conclusion II: red is inside green, green is inside pink, and pink is entirely separate from blue. So no red can be blue at all — some blue are red is not merely unproven, it is impossible.

One follows and one is ruled out, so only conclusion I stands — option (b).

Why the others are wrong

• (a)
  Neither conclusion I nor II follows. — Neither would need conclusion I to fail, but all green are pink and no pink is blue push green and blue apart in every diagram. Conclusion I is a direct chain.
• (c)
  Both conclusions I and II follow. — Both would need some blue to be red. Red lies inside pink, and no pink is blue, so red and blue can never overlap.
• (d)
  Only conclusion II follows. — This keeps the one conclusion the statements actively contradict. Some blue are red cannot survive 'no pink is blue' once red is placed inside pink.

Two rules carry almost every three-statement syllogism. Chaining universals: all A are B plus all B are C gives all A are C. Mixing a universal with a negative: all A are B plus no B is C gives no A is C.

Apply them in order and the diagram draws itself — a nest of circles, red innermost, then green, then pink, with blue standing completely clear of the whole nest.

A 'some' conclusion needs a guaranteed overlap somewhere in the statements. Here every statement is universal and the only relation involving blue is a separation, so no 'some' conclusion touching blue can be reached.

Key facts

• All A are B plus all B are C gives all A are C.
• All A are B plus no B is C gives no A is C.
• 'No pink is blue' converts freely: no blue is pink.
• Universal statements alone cannot produce a 'some' conclusion between classes they keep apart.

Common traps

• Reading 'no pink is blue' as if it still allowed part of blue inside pink.
• Marking a conclusion as following because nothing contradicts it, rather than because the statements force it.

No directly related past PYQ was found.