Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusion/s logically follow/s from the given statements. Statements: All beaches are sand. Some deserts are sand. All mountains are rocky. Conclusions: (I) At least some beaches are desert. (II) At least some sands are rocky.

Correct — A.

Rule: a conclusion follows only if it holds in every diagram the statements allow, not merely in the tidiest one.

Beaches sit wholly inside sand. Deserts overlap sand somewhere. Nothing says the desert part of sand is the beach part, so (I) is a possibility, never a certainty.

The third statement runs mountains into rocky. No statement joins sand to rocky at all, so (II) has no chain to stand on.

Neither conclusion is forced — option (a).

Why the others are wrong

• (b)
  Both conclusions (I) and (II) follows. — Both would have to be unavoidable. Neither is: the beach-desert overlap is optional, and sand is never tied to rocky by any statement.
• (c)
  Only conclusion (I) follows. — (I) treats an optional overlap as a fact. Some deserts are sand does not say which part of sand, so the deserts may miss the beaches entirely.
• (d)
  Only conclusion (II) follows. — (II) needs a route from sand to rocky. Rocky is reached through mountains, and no statement puts mountains anywhere near sand.

This is a three-statement syllogism. Draw circles and ask whether the conclusion survives every arrangement you can legally draw.

Two statements share the term sand: 'All beaches are sand' and 'Some deserts are sand'. In the first, sand is the predicate of an 'all' sentence. In the second, it is the predicate of a 'some' sentence.

In neither case is the whole of sand spoken about, so the shared term cannot fix a link between beaches and deserts. That is the classic undistributed middle.

The third statement sits on a separate chain, mountains to rocky, sharing no term with the other two.

Key facts

• A conclusion follows only if it holds in every diagram consistent with the statements.
• 'All A are B' plus 'Some C are B' leaves B undistributed in both statements, so no definite link between A and C follows.
• 'Some deserts are sand' permits an overlap with beaches but does not assert one.
• Nothing among the three statements connects sand with rocky.

Common traps

• Reading 'Some deserts are sand' as if it named which part of sand the deserts occupy
• Accepting a diagram you happened to draw as proof that a conclusion follows
• Pressing the mountains statement into service although it shares no term with sand

No directly related past PYQ was found.