Syllogisms Questions and Answers

Answer: A

Only conclusion III follows.

All teachers are professors and no professor is male, so no teacher can be male: conclusion III is certain.

About engineers we know only that some males are engineers. Those male engineers cannot be professors, but other engineers, who are not male, may or may not be professors. So 'No engineer is a professor' (I) and 'Some engineers are professors' (II) are both possible but neither is certain. (They are complementary, so exactly one of them is true, but the statements do not tell us which.) That rules out every option containing I or II.

Answer: D

Only conclusions I and III are correct.

'Some soaps are clean' converts directly to 'some clean objects are soaps', which is conclusion I. Those clean soaps are wet, because all clean objects are wet, so at least some wet objects are soaps: conclusion III.

Conclusion II, 'no clean object is a soap', contradicts statement 1. Conclusion IV, 'all wet objects are soaps', does not follow: the statements allow wet objects that are neither clean nor soaps. Since I and III both follow, 'only I' is incomplete, and the 'either ... or' options pair a valid conclusion with an invalid one.

Answer: D

The correct choice is Conclusion I and III follow.

From 'All bottles are glasses' and 'All glasses are jugs', every bottle is a glass and every glass is a jug, so all bottles are jugs: conclusion I follows. 'All bottles are glasses' also means that those glasses which are bottles exist, so 'Some glasses are bottles' follows by conversion: conclusion III follows.

Conclusion II, 'All jugs are bottles', reverses a universal statement. There may be jugs that are not glasses, and glasses that are not bottles, so it does not follow. That rules out every option containing II.

Answer: A

The key gives Only one, counting statement 3 as correct.

Statements 1 and 2 reverse a universal statement. 'All cats are animals' does not mean 'all animals are cats', and 'all dogs are mammals' does not mean 'all mammals are dogs'. Both conclusions are false.

Statement 3 ends in a true conclusion: all parrots are birds. Strictly, 'some birds are parrots' does not by itself prove that every parrot is a bird; the key treats the statement as correct because its conclusion is true, while the conclusions of 1 and 2 are plainly false. On that reading exactly one statement is correct, which rules out 'Only two', 'All three' and 'None'.

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

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.