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: D

The answer is None follows.

The statements say that some officers are aspirants and that all aspirants are girls. Together they give only that some officers are girls. They say nothing at all about boys.

Conclusion I (all officers are boys) and conclusions II and III (some boys are officers, some boys are aspirants) all bring in 'boys', a term that appears in neither statement, so none of them can follow; III even contradicts the statement that all aspirants are girls. Conclusion IV (all aspirants are officers) reverses 'some officers are aspirants' and does not follow either. So every option claiming that one or more conclusions follow is wrong.

Answer: D

The answer is Only II and IV follow.

If all globes are moons and all moons are boxes, every globe is inside the set of moons, which is inside the set of boxes. So all globes are boxes (conclusion II). And since there are globes, and every one of them is a box, some boxes are globes (conclusion IV), by converting II.

Conclusion I (all moons are globes) and conclusion III (all boxes are moons) reverse universal statements, which is not valid: the statements allow moons that are not globes and boxes that are not moons. So the options with I or III, and 'None follows', are wrong.

Answer: C

The valid argument is CEA.

C: A few ones are twos. E: All twos are threes. The ones that are twos are therefore threes, so some ones are threes, which the paper words as A: Many ones are threes. 'Many' and 'a few' are both particular statements here, like 'some'.

• DEB: from 'All fours are threes' and 'All twos are threes' nothing follows about twos and fours; both are merely inside the threes.
• ACE: two particular premises ('many ones are threes', 'a few ones are twos') never give a universal conclusion such as 'all twos are threes'.
• EAC: 'All twos are threes' and 'many ones are threes' only place some ones and all twos among the threes; they need not overlap, so 'a few ones are twos' does not follow.

Answer: C

Both I and II follow.

Conclusion II is the converse of statement 3. A universal negative can be converted directly: if no teacher is an engineer, then no engineer is a teacher.

For conclusion I, statement 2 says some graduates are teachers, and statement 3 says no teacher is an engineer. Those graduates who are teachers are therefore not engineers, so some graduates are not engineers.

Since each conclusion follows on its own, 'Only I', 'Only II' and 'Neither' are all wrong.

Answer: B

Both conclusions (I) and (III) follow.

All phones are laptops and all laptops are pens, so all phones are pens: conclusion (III) follows. Since every phone is a pen, some pens are phones: conclusion (I) follows too.

Computers and phones are both inside laptops, but nothing says the two groups overlap, so 'some computers are phones' does not follow. Every option containing (II) is therefore wrong.