Logical Deduction problems
- 1. Statements: All cars are cats. All fans are cats.
Conclusions:
- All cars are fans
- Some fans are cars.
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 'cats' is not distributed even once in the premises, no definite conclusion follows.
- 2. Statements: All branches are flowers. All flowers are leaves.
Conclusions:
- All branches are leaves.
- All leaves are branches.
- All flowers are branches.
- Some leaves are branches.
Options- A. None follows
- B. Only I and IV follow
- C. Only II and III follow
- D. All follow Discuss
Correct Answer: Only I and IV follow
Explanation:
Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All branches are leaves'. Thus, I follows. IV is the converse of this conclusion and so it also holds.
- 3. Statements: Some bags are pockets. No pocket is a pouch.
Conclusions:
- No bag is a pouch.
- Some bags are not pouches.
- Some pockets are bags.
- No pocket is a bag,
Options- A. None follows
- B. Only I and III follow
- C. Only II and III follow
- D. Only either I or IV follows
- E. All follow Discuss
Correct Answer: Only II and III follow
Explanation:
Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, II follows. III is the converse of the first premise and thus it also holds.
- 4. Statements: All aeroplanes are trains. Some trains are chairs.
Conclusions:
- Some aeroplanes are chairs.
- Some chairs are aeroplanes.
- Some chairs are trains.
- Some trains are aeroplanes.
Options- A. None follows
- B. Only I and II follow
- C. Only II and III follow
- D. Only III and IV follow Discuss
Correct Answer: Only III and IV follow
Explanation:
Since the middle term 'trains' is not distributed even once in the/premises, no definite conclusion follows. However, III is the converse of the second premise while IV is the converse of the first premise. So, both of them hold.
- 5. Statements: All politicians are honest. All honest are fair.
Conclusions:
- Some honest are politicians.
- No honest is politician.
- Some fair are politicians.
- All fair are politicians.
Options- A. None follows.
- B. Only I follows.
- C. Only I and II follow.
- D. Only I and III follow Discuss
Correct Answer: Only I and III follow
Explanation:
Clearly, it follows that 'All politicians are fair'. I is the converse of the first premise, while III is the converse of the above conclusion. So, both I and III hold.
- 6. Statements: Some clothes are marbles. Some marbles are bags.
Conclusions:
- No cloth is a bag.
- All marbles are bags.
- Some bags are clothes.
- No marble is a cloth.
Options- A. Only either I or IV follows
- B. Only either I or II follows
- C. None follows
- D. Only either I or III follows Discuss
Correct Answer: Only either I or III follows
Explanation:
Since both the premises are particular, no definite conclusion follows. However, I and III involve only the extreme terms and form a complementary pair. Thus, either I or III follows.
- 7. Statements: Some tables are TVs. Some TVs are radios.
Conclusions:
- Some tables are radios.
- Some radios are tables.
- All radios are TVs.
- All TVs are tables.
Options- A. None follows
- B. All follow
- C. Only I and III follow
- D. Only II and IV follow Discuss
Correct Answer: None follows
Explanation:
Since both the premises are particular, no definite conclusion follows.
- 8. Statements: All terrorists are guilty. All terrorists are criminals.
Conclusions:
- Either all criminals are guilty or all guilty are criminals.
- Some guilty persons are criminals.
- Generally criminals are guilty.
- Crime and guilt go together.
Options- A. Only I follows
- B. Only I and III follow
- C. Only II follows
- D. Only II and IV follow Discuss
Correct Answer: Only II follows
Explanation:
Since the middle term 'terrorists' is distributed twice in the premises, the conclusion cannot be universal. So, it follows that 'Some guilty persons are criminals'. Thus, II holds.
- 9. Statements: Some books are pens. No pen is pencil.
Conclusions:
- Some pens are books.
- Some pencils are books.
- Some books are not pencils.
- All pencils are books.
Options- A. Only I follows
- B. Only II and III follow
- C. Only I and III follow
- D. Only I and II follow Discuss
Correct Answer: Only I and III follow
Explanation:
Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. Thus, III follows. I is the converse of the first premise and so it also holds.
- 10. Statements: Some bottles are drinks. All drinks are cups.
Conclusions:
- Some bottles are cups.
- Some cups are drinks.
- All drinks are bottles.
- All cups are drinks.
Options- A. Only I and II follow
- B. Only II and III follow
- C. Only II and IV follow
- D. Only III and IV follow
- E. Only I and IV follow Discuss
Correct Answer: Only I and II follow
Explanation:
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bottles are cups'. Thus, I follows. II is the converse of the second premise and so it also holds.
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