Syllogism & Statements — PPSC previous year questions

Every man is mortal (men are a subset of mortals) and Socrates belongs to the set of men, so Socrates must lie inside the set of mortals — the classic syllogism. ```puzzle:venn Socrates in man man in mortal ``` So Socrates is mortal.

Fishes lie wholly outside the circle of birds, and birds lie wholly inside animals, but the premises say nothing about whether fishes lie inside, partly inside or outside animals. So 'no fishes are animals', 'some fishes are animals' and 'all fishes are animals' are each possible but none is forced. ```puzzle:venn fish | bird bird in animal ``` So the relation between fishes and animals cannot be determined.

The statements say only that gold is expensive now and that only the rich are buying it. Nothing is said about future prices, so I is a guess, not a conclusion. The number of shops open has no link to who is buying, so II does not follow either. In statement–conclusion questions only what necessarily follows from the given facts can be accepted. So neither conclusion follows.

Some apples are mangoes and every mango is a vegetable, so the apples that are mangoes must also be vegetables; conclusion I follows. Conclusion II (no mango is an apple) directly contradicts the first statement, so it cannot follow. ```puzzle:venn apple x mango mango in vegetable ``` So only conclusion I follows.

Every athlete likes to run, so an athlete who swims must also like to run: statement II follows for sure. Only some athletes look like gymnasts, so we cannot say all swimmers look like gymnasts (I) or that runners do not (III).

All quiet people are harmless (quiet is a subset of harmless), and no harmless person is easily identified (harmless and easily-identified are disjoint). So no quiet person is easily identified. Option (c) reverses the first premise, and (b) and (d) contradict the second premise. ```puzzle:venn quiet in harmless harmless | easily identified ```

All three premises are particular, and a chain of 'some' relations carries nothing forward: the tigers that are lions need not be the lions that are rabbits, and those rabbits need not be the ones that are horses. So I, II and III all fail, and IV asserts a universal that is nowhere given. ```puzzle:venn tiger x lion lion x rabbit rabbit x horse ``` None follows.

Only the first and third statements mention the sets used in the conclusions. Neither links rooms with flats or apartments. 'Some flats are apartments' links flats and apartments. 'Some halls are rooms' links halls and rooms. The secrets–puzzles statement is unrelated. With no chain between rooms and flats, conclusion 1 cannot be established. Conclusion 2 is equally unsupported, because nothing rules the overlap in or out. ```puzzle:venn flat x apartment secret in puzzle hall x room ``` So neither conclusion follows.

This is a valid categorical syllogism (Barbara form — the 'all A are B, all B are C, so all A are C' pattern): if every apple is a fruit and every fruit is food, then every apple must be food. The conclusion follows necessarily from the premises, so the argument is logically correct. ```puzzle:venn apple in fruit fruit in food ```

This is disjunctive syllogism: P or Q; not P; so Q. 'Either the exam is easy or the students will fail' plus 'the exam was not easy' logically forces 'the students will fail'.