Logical Deduction problems
- 1. Statements: All fish are tortoise. No tortoise is a crocodile.
Conclusions:
- No crocodile is a fish.
- No fish is a crocodile.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either I or II follows
- D. Neither I nor II follows
- E. Both I and II follow Discuss
Correct Answer: Both I and II follow
Explanation:
Since both the premises are universal and one premise is negative, the conclusion must be universal negative. Also, the conclusion should not contain the middle term. So, II follows; I is the converse of II and thus it also holds.
- 2. Statements: Some dedicated souls are angels. All social workers are angels.
Conclusions:
- Some dedicated souls are social workers.
- Some social workers are dedicated souls.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either I or II follows
- D. Neither I nor II follows
- E. Both I and II follow Discuss
Correct Answer: Neither I nor II follows
Explanation:
The first premise is an I type proposition. So, the middle term 'angels' forming the predicate is not distributed. The second premise is an A type proposition. So, the middle term 'angels' forming the predicate is not distributed. Since the middle term is not distributed even once in the premises, no definite conclusion follows.
- 3. Statements: No gentleman is poor. All gentlemen are rich.
Conclusions:
- No poor man is rich.
- No rich man is poor.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either I or II follows
- D. Neither I nor II follows
- E. Both I and II follow Discuss
Correct Answer: Neither I nor II follows
Explanation:
The first premise is an E-type proposition, So, the middle term 'gentleman' forming the subject is distributed. The second premise is an A-type proposition. So, the middle term 'gentlemen' forming the subject is distributed. Since the middle term is distributed twice, the conclusion cannot be universal. Since one premise is negative, the conclusion must be negative. Thus, it follows that 'Some rich men are not poor'. Thus, neither I nor II follows.
- 4. Statements: Some swords are sharp. All swords are rusty
Conclusions:
- Some rusty things are sharp.
- Some rusty things are not sharp.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either I or II follows
- D. Neither I nor II follows
- E. Both I and II follow Discuss
Correct Answer: Only conclusion I follows
Explanation:
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, I follows. Since both the premises are affirmative, the conclusion cannot be negative. Thus, II does not follow.
- 5. Statements: All fishes are grey in colour. Some fishes are heavy.
Conclusions:
- All heavy fishes are grey in colour.
- All light fishes are not grey in colour.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either I or II follows
- D. Neither I nor II follows
- E. Both I and II follow Discuss
Correct Answer: Only conclusion I follows
Explanation:
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some heavy things are grey in colour'. I is a cumulative result of this conclusion and the first premise. Thus, only I holds.
- 6. Statements: All good athletes win. All good athletes eat well.
Conclusions:
- All those who eat well are good athletes.
- All those who win eat well.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either I or II follows
- D. Neither I nor II follows
- E. Both I and II follow Discuss
Correct Answer: Neither I nor II follows
Explanation:
Since the middle term 'good athletes' is distributed twice in the premises, the conclusion must be particular and should not contain the middle term. So it follows that 'Some of those who win, eat well'.
- 7. Statements: All film stars are playback singers. All film directors are film stars.
Conclusions:
- All film directors are playback singers.
- Some film stars are film directors.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either I or II follows
- D. Neither I nor II follows
- E. Both I and II follow Discuss
Correct Answer: Both I and II follow
Explanation:
Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, I follows. II is the converse of the second premise and so it also holds.
- 8. Statements: All hill stations have a sun-set point. X is a hill station.
Conclusions:
- X has a sun-set point.
- Places other than hill stations do not have sun-set points.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either I or II follows
- D. Neither I nor II follows
- E. Both I and II follow Discuss
Correct Answer: Only conclusion I follows
Explanation:
Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, only I follows.
- 9. Statements: Some dreams are nights. Some nights are days.
Conclusions:
- All days are either nights or dreams.
- Some days are nights.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either I or II follows
- D. Neither I nor II follows
- E. Both I and II follow Discuss
Correct Answer: Only conclusion II follows
Explanation:
Since both the premises are particular, no definite conclusion follows. However, II is the converse of the second premise and thus it holds.
- 10. Statements: All jungles are tigers. Some tigers are horses.
Conclusions:
- Some horses are jungles.
- No horse is jungle.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either I or II follows
- D. Neither I nor II follows
- E. Both I and II follow Discuss
Correct Answer: Either I or II follows
Explanation:
Since the middle term 'tigers' is not distributed even once in the premises, no definite conclusion follows. However, I and II involve only the extreme terms and form a complementary pair. So, either I or II follows.
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