Logical Deduction problems
- 1. Statements: Raman is always successful. No fool is always successful.
Conclusions:
- Raman is a fool.
- Raman is not a fool.
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 universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, only II follows.
- 2. Statements: Some desks are caps. No cap is red.
Conclusions:
- Some caps are desks.
- No desk is red.
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 and the other premise is negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some desks are not red'. However, I is the converse of the first premise and thus it holds.
- 3. Statements: Some hens are cows. All cows are horses.
Conclusions:
- Some horses are hens.
- Some hens are horses.
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 one premise is particular, the conclusion must be particular and should not contain the middle term. So, II follows. I is the converse of II and so it also holds.
- 4. Statements: All water is divine. All temples are divine.
Conclusions:
- All water is temple.
- All temples are water.
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 'divine' is not distributed even once in the premises, no definite conclusion can be drawn.
- 5. Statements: All men are dogs. All dogs are cats.
Conclusions:
- All men are cats.
- All cats are men.
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. However, conclusion II, being an A-type proposition, distributes the term 'cats'.
Since the term 'cats' is distributed in II without being distributed in any of the premises, so conclusion II cannot follow. Thus, only I follows.
Since the term 'cats' is distributed in II without being distributed in any of the premises, so conclusion II cannot follow. Thus, only I follows.
- 6. Statements: All young scientists are open-minded. No open-minded men are superstitious.
Conclusions:
- No scientist is superstitious.
- No young people are superstitious.
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 subject in both the conclusions is vague. The true conclusion is 'No young scientist is superstitious'. Thus, neither I nor II follows,
- 7. Statements: Some pastries are toffees. All toffees are chocolates.
Conclusions:
- Some chocolates are toffees.
- Some toffees are not pastries.
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. Thus, it follows that 'Some pastries are chocolates', I is the converse of the second premise and so it holds. Since both the premises are affirmative, the conclusion cannot be negative. Thus, II does not follow.
- 8. Statements: All boys are honest. Sachin is honest.
Conclusions:
- Sachin is a boy.
- All honest persons are boys.
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:
Both the premises are A type propositions. So, the middle term 'honest' forming the predicate in each is not distributed in either. Since the middle term is not distributed even once, no definite conclusion follows.
- 9. Statements: All pens are roads. All roads are houses.
Conclusions:
- All houses are pens.
- Some houses are pens.
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 universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All pens are houses'. II is the converse of this conclusion and so it holds. Since the term 'houses' is distributed in I without being distributed in any of the premises, so I does not follow.
- 10. Statements: All artists are smokers. Some smokers are drunkards.
Conclusions:
- All smokers are artists.
- Some drunkards are not smokers.
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 'smokers' is not distributed even once in the premises, no definite conclusion follows.
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