Syllogisms Questions and Answers

Answer: C

Both 1 and 2 are correct.

Statement 1: all jasmines are flowers and some flowers are white. The white flowers may or may not include jasmines, so 'some jasmines may be white' is a possibility that the premises allow. A definite 'some jasmines are white' would not follow, but 'may be' does.

Statement 2 is a valid chain: all rats are mammals and all mammals are animals, so all rats are animals.

So neither statement oversteps its premises, and the answer is both.

Answer: B

Only two pairs are correctly matched.

Each pair gives a statement and a conclusion drawn by converting it.

• Pair 1: 'All roses are flowers' converts by limitation to 'Some flowers are roses'. Valid.
• Pair 2: 'Some students are athletes' converts only to 'Some athletes are students'; it says nothing about all athletes. Invalid.
• Pair 3: a universal negative converts simply: 'No cats are dogs' means 'No dogs are cats'. Valid.

So pairs 1 and 3 match and pair 2 does not.

Answer: C

The valid sets are 1 and 3.

Set 1: all Ts are squares and all squares are rectangular, so all Ts are rectangular. A valid chain.

Set 3: idiots are bumblers and bumblers fumble, so idiots fumble. Also a valid chain.

Set 2 is invalid: the fat things that are elongated need not be among the elongated things that are huge, so two 'some' premises prove nothing. Set 4 is invalid: water is good for health, but that does not make water a 'health food', and even if it were, 'health foods are rare' would not make water rare. So '4 only' and '1, 2, 3 & 4' are wrong, and '3 only' misses set 1.

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

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.