Syllogism

Directions (Q. 1-5): In each question below there are two statements followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follow(s) from the given statements.

1. Statements: a. All bricks are bakers.
b. Some bakers are horses.
Conclusions: I. Some bricks are bakers.
II. No brick is a baker.
III. Some bricks are horses.
IV. Some horses are bricks.
1) III and IV follow
2) I and III follow
3) I, III and IV follow
4) Either I or II, III and IV follow
5) None of these


2. Statements: a. Some birds are horses.
b. Some horses are bulls.
Conclusions: I. Some birds are bulls.
II. Some horses are birds.
III. Some bulls are horses.
IV. Some bulls are birds.
1) I, II and III follow
2) I and II follow
3) II and III follow
4) III and IV follow
5) All follow

3. Statements: a. All ducks are swans.
b. No bull is a duck.
Conclusions: I. Some swans are not bulls.
II. Some swans are bulls.
III. Some ducks are not bulls.
IV. Some bulls are ducks.
1) Either I or II follows
2) I and III follow
3) III and either I or II follow
4) Either I or II and IV follow
5) None of these

4. Statements: a. All birds are tables.
b. Some books are birds.
Conclusions: I. Some books are tables.
II. Some birds are books.
III. Some tables are birds.
IV. Some tables are books.
1) Only II and III follow
2) I, II and III follow
3) II, III and IV follow
4) Only I and IV follow
5) All follow

5. Statements: a. Only books are worms.
b. Only dogs are books.
Conclusions: I. All worms are dogs.
II. All dogs are worms.
III. Some worms are not dogs.
IV. Some dogs are not worms.
1) I and either II or IV follow
2) II and either I or III follow
3) I and II follow
4) Any two out of I, II, III and IV follow
5) Either I or III, and either II or IV follow

Answers
1. 5; II is wrong while I is true because of the first statement.
III and IV are not certain because no conclusion can be established between ‘bricks’ and ‘horses’ because the rule says: A + I = no conclusion. So, only I follows is the correct answer.

2. 3; No conclusion is established between ‘birds’ and ‘bulls’ by the rule : I+I = no conclusion. But conclusion II directly follows from the first statement while conclusion III directly follows from the second statement.

3. 2; Rearrange the sentences as:
(i) No bull is a duck. (Type E)
(ii) All ducks are swans (Type A)
Now the sentences are aligned. Now, by the rule E + A = O reversed, conclusion I follows. Further, conclusion III is directly supported by the second statement (ie No bull is a duck.)

4. 5; Rearrange the sentences to align them:
(i) Some books are birds (Type I)
(ii) All birds are tables (Type A)
Now, the sentences are aligned. Now, by the rule I + A = I, conclusion I is proved. Further, conclusion IV directly follows from conclusion I. Conclusion II independently follows from the second statement while conclusion III directly follows from the first statement.

5. 1; Only A are B is an “exclusive”-type proposition which can be converted to type A as All B are A. Hence, the given statement may be canverted to two statements type A, i.e. All worms are books and All books are dogs. Now A+A = A. Hence conclusion I follows. Further, conclusion II and IV make an A-O pair which is a
complementary pair; so at least one of these must always
be true. Hence, choice (1) is correct.


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