Read the given statements and conclusions carefully. You have to take the given statements to be true 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 fruit are sour. Some sour are vegetables. Some vegetables are green. Conclusions: (I) All vegetables are sour. (II) Some sour are green.

Correct — A. Test each conclusion by trying to draw a diagram that makes it false. One such diagram is enough to reject it.

Rule: a 'some' premise never licenses an 'all' conclusion, and two 'some' premises together license nothing.

Conclusion (I) turns 'Some sour are vegetables' into 'All vegetables are sour'. That premise leaves room for vegetables sitting outside the sour circle, so (I) does not follow.

Conclusion (II) chains 'Some sour are vegetables' with 'Some vegetables are green'. The sour vegetables and the green vegetables can be entirely different vegetables, so no overlap of sour and green is forced.

Neither follows — which is option (a).

Why the others are wrong

• (b)
  Both conclusions (I) and (II) follow — Both cannot follow, because (I) is the converse of a 'some' premise. 'Some sour are vegetables' gives back only 'Some vegetables are sour'.
• (c)
  Only conclusion (II) follows — (II) fails as well. The middle term vegetables is undistributed in both premises, so the two 'some' groups need never meet.
• (d)
  Only conclusion (I) follows — (I) is blocked outright. No premise says anything about all vegetables — 'Some sour are vegetables' constrains only part of the sour group.

Syllogism items are decided by the weakest reading the statements allow. If one legal Venn diagram breaks a conclusion, that conclusion does not follow, however plausible it sounds.

Two rules settle most such items. A particular premise cannot be converted into a universal: 'Some A are B' gives back 'Some B are A' and nothing stronger. And two particular premises yield no conclusion, because the middle term is undistributed on both sides.

Here 'All fruit are sour' is never needed at all: neither conclusion mentions fruit.

Key facts

• Some A are B converts only to Some B are A, never to All B are A.
• Two particular (some) premises never yield a valid conclusion.
• A conclusion is rejected the moment one consistent diagram makes it false.

Common traps

• Accepting (II) because both premises contain the word vegetables.
• Importing real-world knowledge about which vegetables are sour.
• Converting 'Some sour are vegetables' into 'All vegetables are sour'.

No directly related past PYQ was found.