Syllogisms Questions and Answers

Answer: D

The definite conclusion is Some cricket players are hockey players.

Some cricket players are tennis players, and every tennis player is a hockey player. So those cricket players who play tennis are certainly hockey players, which means at least some cricket players are hockey players.

'All cricket players are hockey players' does not follow, because the cricketers who do not play tennis may or may not play hockey. 'Some cricket players are not hockey players' is only possible, not certain. 'Some tennis players are not hockey players' contradicts the second statement.

Answer: B

If 'No S is P' is false, then Some S is P is necessarily true.

In traditional logic, 'No S is P' (a universal negative, E) and 'Some S is P' (a particular affirmative, I) are contradictories: exactly one of them is true. So when 'No S is P' is false, 'Some S is P' must be true.

'All S is P' may or may not be true: it is possible that only some S are P. 'Some S is not P' is also undetermined, since every S might be P. Only 'Some S is P' follows necessarily, so 'None of the above' is wrong too.

Answer: B

The conclusion that is not valid is Some teachers are not Mathematicians.

From the premises: every teacher is a graduate, no graduate is poor, so no teacher is poor (option c follows). All poets are poor, so no poet is a graduate and hence no poet is a teacher (option d follows). Some mathematicians are poets, and those cannot be teachers, so some mathematicians are not teachers (option a follows).

Nothing in the argument says anything about teachers who are not mathematicians; all teachers might be mathematicians who are not poets. So option (b) does not follow.

Answer: D

The answer is Neither Conclusion I nor II follows.

All desktops are computers, but only some computers are machines. The computers that are machines need not include any desktops, so 'Some desktops are machines' is possible but not certain. Conclusion I does not follow.

Some laptops are computers and all desktops are computers, but two groups both lying inside 'computers' need not overlap. 'Some laptops are desktops' is likewise only a possibility, so Conclusion II does not follow either.

Answer: C

Only (ii) and (iii) follow.

(ii) follows: all circles are triangles, so some triangles must be circles. (iii) follows: all squares are rectangles, so some squares are rectangles.

(i) does not follow. All squares are rectangles and no triangle is a rectangle, so no triangle can be a square. (iv) does not follow either: circles are triangles and no triangle is a rectangle, so no circle is a rectangle, and since every square is a rectangle, no square can be a circle.

Answer: C

Correct answer: C

In C the middle term is properly distributed: all women are men and all men can run, so all women can run - the third segment does follow from the two before it. In A and B the middle term appears as a predicate in both premises, which proves nothing: two classes both contained in a third need not overlap.

Answer: C

Correct answer: Only III follows

Some libraries are temples and all temples are books, so some libraries are books - conclusion III. Conclusions I and II both try to reach pens, and the only statement about pens is a particular one, which cannot carry a conclusion. Only III follows.

Answer: D

Correct answer: If neither conclusion I nor II follows

Both statements are particular, and the texts that are books need not be the texts that are copies, so nothing links books to copies. Conclusion II makes a universal out of a particular. Neither follows.

Answer: A

Correct answer: If only conclusion I follows

Some leaves are vacations gives its converse, some vacations are leaves - conclusion I. Conclusion II excludes every leave from holidays, whereas only the vacations are excluded, and some leaves may be neither. Only I follows.

Answer: D

Correct answer: Both I and II follow

Every photograph is a portrait and every portrait an artwork, so every photograph is an artwork - conclusion I. And since every portrait is an artwork, some artworks are portraits - conclusion II, the converse. Both follow.