Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: Some cups are glasses. No glass is a stone. All stones are metals. Conclusions: I. All cups can never be stones. II. No cup is a metal. III. All metals can never be glasses.

Correct — B. Two of these conclusions are 'can never be' claims, which follow when the statements make the matching 'all' impossible.

Rule: find one member of the subject class that provably sits outside the predicate class.

I. Some cups are glasses and no glass is a stone, so that cup is not a stone. 'All cups are stones' is impossible, so I follows.

II. Nothing connects cups to metals. A cup outside the glass overlap may be a stone, and every stone is a metal, so II fails.

III. All stones are metals and no glass is a stone, so a stone is a metal that is not a glass. 'All metals are glasses' is impossible, so III follows.

That leaves I and III — option (b).

Why the others are wrong

• (a)
  Only II and III conclusion follow — III is sound, but II asserts a separation the statements never draw. No premise keeps cups out of metals, and a cup that is not a glass is free to be a stone, and so a metal.
• (c)
  Only conclusion I follows — I is right, but this option drops III. All stones are metals while no glass is a stone, so at least one metal is not a glass, which blocks 'all metals are glasses'.
• (d)
  All I, II and III conclusion follow — This option carries II, and II is the one conclusion the premises leave open. 'No cup is a metal' needs a stated separation between cups and metals, and none is given.

A 'can never be' conclusion is a statement about possibility, and it is judged differently from an ordinary categorical one.

'All X can never be Y' follows when the statements make it impossible for every X to be Y. One X provably outside Y settles it. It does not require that no X is Y.

Conclusion I needs a single cup that is not a stone, and the cups-glasses overlap supplies one. Conclusion III needs a single metal that is not a glass, and a stone supplies one.

Conclusion II is a flat negative, 'No cup is a metal', and a flat negative needs an explicit separation somewhere in the premises.

Key facts

• 'All X can never be Y' is established by showing one X that must lie outside Y.
• Some cups are glasses and no glass is a stone, so at least one cup is not a stone.
• All stones are metals and no glass is a stone, so at least one metal is not a glass.
• A conclusion of the form 'No X is Y' requires an explicit separation in the statements.

Common traps

• Reading 'All cups can never be stones' as if it meant 'No cup is a stone'.
• Assuming two classes are separate merely because no premise joins them.
• Forgetting that 'All stones are metals' guarantees stones exist under the exam's convention.

No directly related past PYQ was found.