Syllogisms Questions and Answers

Answer: C

The answer is Either conclusion I or II follows.

From 'No bird is pen' and 'All pens are hills', nothing definite follows about birds and hills: some hills may or may not be birds. So neither I ('Some hills are birds') nor II ('No hill is bird') follows by itself.

But I and II are a complementary pair about the same two terms: one says some hills are birds, the other that none is. Exactly one of them must be true, so the answer is 'either I or II'. Conclusion III ('Some tables are pens') does not follow, because the tables that are birds cannot be pens, and nothing is said about other tables.

Answer: D

The statements that follow with certainty are (i), (ii) and (iii).

If “Some human beings are not cruel creatures” is false, then there is no human being who is not cruel, so all human beings are cruel creatures: statement (i).

Human beings exist in this world (they are among its creatures), so if all of them are cruel, then some human beings are cruel (ii), and equally some cruel creatures are human beings (iii), which is (ii) read the other way round.

Statement (iv), “No human beings are cruel creatures”, contradicts (i), so any option containing it is wrong. Options listing only (i), or only (i) and (ii), leave out statements that also follow.

Answer: C

The correct option is only conclusion I and conclusion III are correct.

Conclusion I is the converse of Statement 1: if some engineers are writers, then those same people are writers who are engineers, so some writers are engineers. Conclusion III is the converse of Statement 2: “No writer is an actor” means writers and actors do not overlap at all, so no actor is a writer.

Conclusion II does not follow: all actors are engineers, but that does not make all engineers actors. Conclusion IV contradicts Statement 2, so it is false, and the “either III or IV” option is wrong because III is definitely true and IV definitely false, not an either-or pair. Only I is incomplete, since III also follows.

Answer: D

Neither (i) nor (ii) follows.

“All hill-stations have a lake” means every hill-station has at least one lake. It sets a minimum, not a maximum, so a hill-station with two lakes still satisfies it.

Statement (i) does not follow: having two lakes does not stop Ooty from being a hill-station, and nothing says whether it is one. Statement (ii) does not follow either: the premise never limits a hill-station to one lake. Both rest on reading “a lake” as “exactly one lake”.

Answer: B

Only conclusion ii follows.

Some shelves are chairs, and all chairs are benches, so those shelves that are chairs are also benches: at least one shelf is a bench (ii).

The other conclusions do not follow. The tables that are shelves need not be the same shelves that are chairs, so no table need be a bench or a chair, which rules out i and iii. 'All chairs are benches' does not mean 'all benches are chairs'; benches may include things that are not chairs, so iv fails.

That makes 'Only ii' correct, and every option including i, iii or iv wrong.

Answer: D

The certain inference is Some ferocious creatures are creatures with claws.

The passage says creatures with claws exist ('there are also creatures that have claws') and that all of them are ferocious. So at least one ferocious creature has claws, which is exactly the statement.

'All creatures with claws are animals' does not follow: we know animals are ferocious and clawed creatures are ferocious, but nothing says the clawed creatures are animals. 'Some creatures with claws are non-ferocious' and 'some non-ferocious creatures have claws' both contradict the rule that every clawed creature is ferocious.

Answer: C

Neither conclusion I nor II follows.

Statement I keeps managers and leaders apart; statement II puts all leaders inside the set of executives. Nothing says anything about managers and executives directly: managers may be executives who are not leaders, or they may not be executives at all.

So 'No manager is an executive' does not follow, and neither does 'No executive is a manager', which says the same thing. Both are possible but not certain, so options claiming either or both follow are wrong.

Answer: A

The answer is Only conclusion I and conclusion II are correct.

Conclusion I: the bottles that are cups are, like every cup, knives, so some bottles are knives. Conclusion II: since every cup is a knife and cups exist, some knives are cups; this is the converse of 'All cups are knives' restricted to 'some'.

Conclusion III does not follow: only some bottles are known to be cups, and nothing says every cup is a bottle. Conclusion IV reverses 'All cups are knives'; there may be knives that are not cups. So any option containing III or IV is wrong.

Answer: B

The valid inferences are Only II and III.

From 'all heroes are winners' and 'all winners are lucky', every hero is lucky. So, assuming heroes exist as the usual reading of such statements does, some lucky people are heroes (II), and some winners are heroes (III), the converse of statement 1 limited to 'some'.

I does not follow: the lucky people may include many who are not heroes, so 'all lucky people are heroes' reverses the inclusion. Every option containing I is therefore wrong, and 'Only III' leaves out II, which follows just as directly.

Answer: C

The valid inference is If (i) and (ii) are true, then (iii) is true.

If some roses are red and all red flowers fade quickly, then those red roses fade quickly, so some roses fade quickly.

The other options try to infer something from a false premise, which does not work. If (ii) is false, some red flowers may still fade quickly, and other roses may too, so (iii) could be either true or false; neither "then (iii) is false" nor "then (iii) is true" follows. Likewise, if (i) and (ii) are both false, nothing is settled about whether some roses fade quickly.