Take the given statements to be true, even if they differ from commonly known facts. Then decide which of the conclusions follow logically from them, and choose the correct option. Where there are two conclusions, the options mean: (A) Only (1) follows. (B) Only (2) follows. (C) Either (1) or (2) follows. (D) Neither (1) nor (2) follows. (E) Both (1) and (2) follow.
Question 1
Statements:
Some birds are fliers.
Some fliers are insects.
Conclusions:
1. Some birds are insects.
2. No bird is an insect.
Which conclusion(s) follow logically?
Some birds are fliers.
Some fliers are insects.
Conclusions:
1. Some birds are insects.
2. No bird is an insect.
Which conclusion(s) follow logically?
Explanation
The statements do not decide whether birds and insects overlap, so neither conclusion follows on its own. But (1) and (2) are a complementary pair ("some" and "none") about the same two terms, so one of them must be true. Hence either (1) or (2) follows.
Question 2
Statements:
Some pens are cups.
Some cups are plates.
Conclusions:
1. Some pens are plates.
2. Some plates are pens.
Which conclusion(s) follow logically?
Some pens are cups.
Some cups are plates.
Conclusions:
1. Some pens are plates.
2. Some plates are pens.
Which conclusion(s) follow logically?
Explanation
Two "some" statements never give a definite link between the two outer terms, so neither conclusion follows.
Question 3
Statements:
All boxes are bags.
All bags are trunks.
Some trunks are cases.
Conclusions:
1. Some cases are trunks.
2. All boxes are trunks.
3. Some boxes are cases.
4. Some bags are cases.
Which conclusion(s) follow logically?
All boxes are bags.
All bags are trunks.
Some trunks are cases.
Conclusions:
1. Some cases are trunks.
2. All boxes are trunks.
3. Some boxes are cases.
4. Some bags are cases.
Which conclusion(s) follow logically?
Explanation
(1) is the valid reversal of "some trunks are cases", and (2) follows by chaining the first two statements. Boxes and bags are not linked to cases, so (3) and (4) do not follow.
Question 4
Statements:
All cats are mammals.
Some mammals are pets.
Some pets are birds.
Conclusions:
1. Some pets are cats.
2. Some birds are mammals.
3. Some cats are pets.
4. Some birds are cats.
Which conclusion(s) follow logically?
All cats are mammals.
Some mammals are pets.
Some pets are birds.
Conclusions:
1. Some pets are cats.
2. Some birds are mammals.
3. Some cats are pets.
4. Some birds are cats.
Which conclusion(s) follow logically?
Explanation
Two "some" links in a row do not connect the outer terms, and the cats are only known to be inside mammals. So none of the four conclusions follows.
Question 5
Statements:
All pens are tools.
Some tools are knives.
Some knives are blades.
Conclusions:
1. Some blades are knives.
2. Some pens are knives.
3. Some tools are pens.
4. Some pens are blades.
Which conclusion(s) follow logically?
All pens are tools.
Some tools are knives.
Some knives are blades.
Conclusions:
1. Some blades are knives.
2. Some pens are knives.
3. Some tools are pens.
4. Some pens are blades.
Which conclusion(s) follow logically?
Explanation
(1) and (3) are valid reversals ("some knives are blades" and "all pens are tools"). A chain of "all", "some" and "some" does not link pens to knives or blades, so (2) and (4) do not follow.
Question 6
Statements:
Some boys are players.
Some players are singers.
All singers are artists.
Conclusions:
1. Some artists are players.
2. Some singers are boys.
3. No singer is a boy.
4. Some players are boys.
Which conclusion(s) follow logically?
Some boys are players.
Some players are singers.
All singers are artists.
Conclusions:
1. Some artists are players.
2. Some singers are boys.
3. No singer is a boy.
4. Some players are boys.
Which conclusion(s) follow logically?
Explanation
(1) follows because some players are singers and all singers are artists. (4) is the reversal of the first statement. Nothing links boys and singers, but (2) and (3) are a complementary pair ("some" and "none"), so exactly one of them must be true. Hence (1), (4) and either (2) or (3) follow.
Question 7
Statements:
All cars are vehicles.
No vehicle is a plant.
Conclusions:
1. No car is a plant.
2. No plant is a car.
3. Some cars are plants.
4. Some plants are vehicles.
Which conclusion(s) follow logically?
All cars are vehicles.
No vehicle is a plant.
Conclusions:
1. No car is a plant.
2. No plant is a car.
3. Some cars are plants.
4. Some plants are vehicles.
Which conclusion(s) follow logically?
Explanation
(1) follows directly, and (2) is the valid reversal of a "no" statement. (3) and (4) both contradict "no vehicle is a plant". So only (1) and (2) follow.
Question 8
Statements:
All shirts are cloths.
No cloth is plastic.
Conclusions:
1. All cloths are shirts.
2. Some plastics are shirts.
3. No shirt is plastic.
4. Some shirts are plastic.
Which conclusion(s) follow logically?
All shirts are cloths.
No cloth is plastic.
Conclusions:
1. All cloths are shirts.
2. Some plastics are shirts.
3. No shirt is plastic.
4. Some shirts are plastic.
Which conclusion(s) follow logically?
Explanation
Shirts are inside cloths and no cloth is plastic, so no shirt is plastic (3). Conclusions (2) and (4) contradict this, and (1) is an invalid reversal.
Question 9
Statements:
All sparrows are birds.
Some singers are birds.
Conclusions:
1. Some birds are singers.
2. All singers are sparrows.
3. All sparrows are singers.
4. Some singers are sparrows.
Which conclusion(s) follow logically?
All sparrows are birds.
Some singers are birds.
Conclusions:
1. Some birds are singers.
2. All singers are sparrows.
3. All sparrows are singers.
4. Some singers are sparrows.
Which conclusion(s) follow logically?
Explanation
Only the reversal of "some singers are birds" follows, giving (1). Birds is the middle term in both statements without being distributed in a way that links sparrows to singers, so (2), (3) and (4) do not follow.
Question 10
Statements:
All doctors are graduates.
Some teachers are graduates.
Conclusions:
1. All doctors are teachers.
2. All teachers are doctors.
3. Some graduates are teachers.
4. All graduates are doctors.
Which conclusion(s) follow logically?
All doctors are graduates.
Some teachers are graduates.
Conclusions:
1. All doctors are teachers.
2. All teachers are doctors.
3. Some graduates are teachers.
4. All graduates are doctors.
Which conclusion(s) follow logically?
Explanation
Only the reversal of "some teachers are graduates" is certain, giving (3). Doctors and teachers are not linked, so (1) and (2) do not follow, and graduates need not all be doctors, so (4) does not follow.
Question 11
Statements:
Some chairs are wooden.
Some tables are chairs.
Conclusions:
1. Some tables are wooden.
2. Some chairs are tables.
Which conclusion(s) follow logically?
Some chairs are wooden.
Some tables are chairs.
Conclusions:
1. Some tables are wooden.
2. Some chairs are tables.
Which conclusion(s) follow logically?
Explanation
"Some tables are chairs" reverses validly to "some chairs are tables" (2). Two "some" statements do not link tables to wooden things, so (1) does not follow. Only (2) follows.
Question 12
Statements:
Some apples are red.
Some fruits are apples.
Conclusions:
1. Some apples are sweet.
2. All fruits are red.
Which conclusion(s) follow logically?
Some apples are red.
Some fruits are apples.
Conclusions:
1. Some apples are sweet.
2. All fruits are red.
Which conclusion(s) follow logically?
Explanation
Nothing is said about sweetness, so (1) does not follow. Two "some" statements never give a universal conclusion, so (2) does not follow. Neither follows.
Question 13
Statements:
All cups are plates.
All plates are dishes.
Conclusions:
1. All cups are dishes.
2. Some dishes are cups.
Which conclusion(s) follow logically?
All cups are plates.
All plates are dishes.
Conclusions:
1. All cups are dishes.
2. Some dishes are cups.
Which conclusion(s) follow logically?
Explanation
Chaining the two statements gives "all cups are dishes" (1). Since all cups are dishes, some dishes are cups (2) also follows. Both follow.
Question 14
Statements:
All pens are tools.
All tools are metals.
Conclusions:
1. All metals are tools.
2. All pens are metals.
Which conclusion(s) follow logically?
All pens are tools.
All tools are metals.
Conclusions:
1. All metals are tools.
2. All pens are metals.
Which conclusion(s) follow logically?
Explanation
Pens are inside tools and tools are inside metals, so all pens are metals (2) follows. The reverse, "all metals are tools" (1), does not follow.
Question 15
The question given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.
Statement - A. All beggars are poor. All lions are poor. So, all lions are beggars.
B. All people are boxes. All foxes are people. So, all boxes are foxes.
C. All men can run. All women are men. So, all women can run.
Statement - A. All beggars are poor. All lions are poor. So, all lions are beggars.
B. All people are boxes. All foxes are people. So, all boxes are foxes.
C. All men can run. All women are men. So, all women can run.
Explanation
In C, all men can run and all women are men, so all women can run. It needs both statements. In A, from all beggars are poor and all lions are poor it cannot follow that all lions are beggars. In B, from all people are boxes and all foxes are people it cannot follow that all boxes are foxes. So only C is correct.
Question 16
In the question given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.
Statement - A. All cats are mad. All sick persons are mad. So, all sick persons are cats.
B. All oranges are white. All figs are oranges. So, all figs are white.
C. No man can crawl. No kite can crawl. So, all men are kites.
Statement - A. All cats are mad. All sick persons are mad. So, all sick persons are cats.
B. All oranges are white. All figs are oranges. So, all figs are white.
C. No man can crawl. No kite can crawl. So, all men are kites.
Explanation
In B, all oranges are white and all figs are oranges, so all figs are white. It needs both statements. In A, from all cats are mad and all sick persons are mad it cannot follow that all sick persons are cats. In C, from two negative statements nothing follows. So only B is correct.
Question 17
The question given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.
Statement - A. No Z is A. All X is Z. No X is A.
B. No Z is A. All X is Z. All X is A.
C. Some Z is not A. Some X is Z. Some X is not A.
Statement - A. No Z is A. All X is Z. No X is A.
B. No Z is A. All X is Z. All X is A.
C. Some Z is not A. Some X is Z. Some X is not A.
Explanation
In A, no Z is A and all X is Z, so all X is in Z and therefore no X is A. This follows only when both statements are used. In B, from no Z is A and all X is Z it cannot follow that all X is A. In C, from some Z is not A and some X is Z it cannot follow that some X is not A. So only A is correct.
Question 18
In the question given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.
Statement - A. Ravens are white. Ravens are good. All good are white.
B. Insects are faster than hawks. All eagles are hawks. Insects are faster than eagles.
C. No boy is a saint. Peter is a boy. Peter is a saint.
Statement - A. Ravens are white. Ravens are good. All good are white.
B. Insects are faster than hawks. All eagles are hawks. Insects are faster than eagles.
C. No boy is a saint. Peter is a boy. Peter is a saint.
Explanation
In B, insects are faster than hawks, and all eagles are hawks, so insects are faster than eagles. This needs both statements. In A, the third statement does not follow from the first two. In C, from "no boy is a saint" and "Peter is a boy" we get that Peter is not a saint, not that Peter is a saint. So only B is correct.
Question 19
In the question below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.
Statement - A. All ugly things are happy. She is ugly. She is happy.
B. All nice things are flat. TVs are flat. TVs are nice things.
C. Potatoes are balls. All balls are fruits. Potatoes are fruits.
Statement - A. All ugly things are happy. She is ugly. She is happy.
B. All nice things are flat. TVs are flat. TVs are nice things.
C. Potatoes are balls. All balls are fruits. Potatoes are fruits.
Explanation
In A, all ugly things are happy and she is ugly, so she is happy. This follows only when both statements are used. In C, potatoes are balls and all balls are fruits, so potatoes are fruits. This also uses both. In B, from all nice things are flat and TVs are flat we cannot say that TVs are nice things. So A and C are correct.
Question 20
In the question given below consists of five or six statements followed by options consisting of three statements put together in a specific order. Choose the option which indicates a valid argument containing logically related statements that is, where the third statement is conclusion drawn from preceding two statements.
Statement - A. Cars are birds.
B. Some birds are ants.
C. Cars are ants.
D. Some Cars are ants.
E. Some Cars are not ants.
F. No car is ant.
Statement - A. Cars are birds.
B. Some birds are ants.
C. Cars are ants.
D. Some Cars are ants.
E. Some Cars are not ants.
F. No car is ant.
Explanation
In A, D, B: cars are birds (A), some cars are ants (D), so some birds are ants (B). The conclusion follows from the first two statements. The other options do not give a valid conclusion.
Question 21
In the question given below consists of five or six statements followed by options consisting of three statements put together in a specific order. Choose the option which indicates a valid argument containing logically related statements that is, where the third statement is conclusion drawn from preceding two statements.
A. An eagle lays eggs.
B. All birds lay eggs.
C. Some birds can fly.
D. An eagle cannot fly.
E. An eagle is a bird.
F. An eagle cannot swim.
A. An eagle lays eggs.
B. All birds lay eggs.
C. Some birds can fly.
D. An eagle cannot fly.
E. An eagle is a bird.
F. An eagle cannot swim.
Explanation
In the set B, E, A: all birds lay eggs (B), an eagle is a bird (E), so an eagle lays eggs (A). The third statement follows from the first two. The other options do not give a valid conclusion.
Question 22
Statement - A. Some drugs are illegal. Marble is illegal. Marble is a drug.
B. All wolves are dogs. Some dogs are birds. Some wolves are dogs.
C. All locks are keys. Some keys do not open. Some locks do not open.
B. All wolves are dogs. Some dogs are birds. Some wolves are dogs.
C. All locks are keys. Some keys do not open. Some locks do not open.
Explanation
In A, from some drugs are illegal and Marble is illegal we cannot say that Marble is a drug. In B, the third statement follows from the first alone (all wolves are dogs, so some wolves are dogs), and not from both together. In C, from all locks are keys and some keys do not open we cannot say that some locks do not open. So none of the sets is correct.
Question 23
In given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.
Statement - A. Many writers are not readers. All plumbers are writers. Some plumbers are not readers.
B. Boys play cricket. Some girls do not play cricket. Some girls are not boys.
C. All Humans live in houses. Some penguins live in houses. Some penguins are Humans.
Statement - A. Many writers are not readers. All plumbers are writers. Some plumbers are not readers.
B. Boys play cricket. Some girls do not play cricket. Some girls are not boys.
C. All Humans live in houses. Some penguins live in houses. Some penguins are Humans.
Explanation
In B, all boys play cricket, and some girls do not play cricket. Those girls are not among the boys, so some girls are not boys, and this conclusion uses both statements. In A, from all plumbers are writers and many writers are not readers, we cannot say that some plumbers are not readers. In C, from all humans live in houses and some penguins live in houses, we cannot say that some penguins are humans. So only B is correct.
Question 24
Statements:
All Lawyers are extrovert.
Some wise men are extrovert.
Conclusions:
(a) All lawyers are wise men.
(b) All wise men are lawyers.
(c) Some extrovert are wise men.
(d) All extrovert are lawyers.
Which conclusion(s) follow logically?
All Lawyers are extrovert.
Some wise men are extrovert.
Conclusions:
(a) All lawyers are wise men.
(b) All wise men are lawyers.
(c) Some extrovert are wise men.
(d) All extrovert are lawyers.
Which conclusion(s) follow logically?
Explanation
"Some wise men are extrovert" converts validly to "some extrovert are wise men" (conclusion c). No premise connects lawyers and wise men directly, so (a) and (b) do not follow, and the universal "all lawyers are extrovert" cannot be validly reversed to "all extrovert are lawyers" (d).
