Syllogisms Questions and Answers

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: 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: D

Only IV follows.

Conclusion IV, 'Some trees are not sharks', is statement (A) itself, so it follows.

The others do not. Statement (B) says some sharks are not balloons, which directly contradicts I, 'All sharks are balloons'. Nothing in the statements links balloons to trees, so neither II ('All balloons are trees') nor III ('Some trees are balloons') can be concluded. Two negative particular statements give no definite conclusion between trees and balloons.

I and III do not form an either-or pair, because they are not about the same two terms, so 'Only either I or III follows' is also wrong.

Answer: D

Only I, II and IV follow.

I: 'Some google are cottons' converts to 'Some cottons are google', so I follows.

II: the google that are cottons cannot be pillows, because no cottons are pillow. So some google are not pillow, and II follows.

IV: 'No cottons are pillow' means every cotton is outside pillow, and since some cottons exist (statement A), some cottons are not pillow. IV follows.

III, 'Some pillow are google', does not follow: the statements put no pillow inside google. So any option leaving out II or IV, or including III, is wrong.

Answer: A

Only I, II and IV follow.

I: some gadgets are buffaloes, and all buffaloes are witches, so those gadgets are witches. 'Some gadgets are witches' follows.

II and IV: 'All buffaloes are witches' gives 'Some buffaloes are witches' (IV) and, by conversion, 'Some witches are buffaloes' (II). Both follow.

III, 'All witches are buffaloes', reverses the universal statement, which is not allowed: there may be witches that are not buffaloes. 'Only I & II' leaves out IV, 'Only I & III' includes III, and II and III are not an either-or pair.

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”.