Syllogism problems
- 1. Statements:
All University Professors have a doctorate degree. X is a lady professor.
Conclusions:
I. X does not have a Doctorate degree.
II. Only men Professors have a Doctorate degree.
Options- A. Both I & II follow
- B. Only I follows
- C. Neither I nor II follows
- D. Only II follows Discuss
Correct Answer: Neither I nor II follows
Explanation:
Both the premises are Universal Affirmative. We can align the premises by changing their order. Thus,
X is a lady professor. ? All University professors have a doctorate degree.
We know that,
A + A ? A - type conclusion. Thus our derived conclusion would be "X has a doctorate degree".
- 2. Statement:
All philosophers are men. Socrates was a philosopher. Conclusion:
I. Socrates was a man.
II. Women cannot become philosophers.
Options- A. Only I is valid
- B. Only II is valid
- C. Both are not valid
- D. Both are valid Discuss
Correct Answer: Both are valid
Explanation:
All philosophers without exception are men. So no woman can be philosopher.
- 3. No monkey can sing but some monkeys can talk.
If the above statement is correct, then which of the following is correct?
Options- A. Some monkeys may sing
- B. All monkeys can't sing
- C. All monkeys can't talk
- D. All monkeys can talk Discuss
Correct Answer: All monkeys can't sing
Explanation:
Clearly, all monkeys cannot sign.
- 4. Statements:
(A) No cow is a chair.
(B) All chairs are tables.
Conclusions:
I. Some tables are chairs.
II. Some tables are cows.
III. Some chairs are cows.
IV. No table is a cow.
Options- A. Either II or III follow
- B. Either II or IV follow
- C. Only I follows
- D. \All conclusions follow Discuss
Correct Answer:
Explanation:
First Premise is Universal Negative (E-type).
Second Premise is Universal Affirmative (A-type).
No cow is chair. ? All chairs are tables.
E + A ? O1 ? type of Conclusion "Some tables are not cows."
Conclusion I is Converse of the second Premise. Therefore, Conclusion I follows.
Conclusions II and IV form Complementary Pair. Therefore, either Conclusion II or IV follows. Thus, Conclusion I and Conclusion II or IV follow.
There is no such options.
- 5. Statements:
No man is intelligent.
All women are intelligent.
Conclusions:
I. No man is a woman.
II. No woman is a man.
Options- A. Only I follows
- B. Only II follows
- C. Both I & II follow
- D. Neither of them follow Discuss
Correct Answer: Both I & II follow
Explanation:
First Premise is Universal Negative (E-type).
Second Premise is Universal Affirmative (A-type).
We can align the Premises by Converting the first Premise and changing their order. Thus,
All women are intelligent. ? No intelligent is a man .
we know that,
A + E ?E-type Conclusion Thus our derived Conclusion would be:
"No woman is a man"
This is the Conclusion II. Conclusion I is the Converse of this Conclusion.
Therefore, both the Conclusions I and II follow.
- 6. Statements:
All carts are cars.
All cars are trains. So
Conclusions:
I. All carts are trains.
II. All trains are carts.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Both conclusions I and II follow
- D. Neither conclusion I nor conclusion II follows Discuss
Correct Answer: Only conclusion I follows
Explanation:
Both the Premises are Universal Affirmative (A?type).
All carts are cars. ? All cars are trains.
A + A ? A-type of Conclusion
"All carts are trains."
This is Conclusion I.
- 7. Statements:
All soldiers are men.
Some citizens are soldiers.
Conclusions:
I. Some citizens are men.
II. All soldiers are citizens.
Options- A. Only I follows
- B. Neither I nor II follows
- C. Only II follows
- D. Both I and II follow Discuss
Correct Answer: Only I follows
Explanation:
We can align the premises by changing their order:
Some citizens are solidiers. ? All solidiers are men.
We know that
I + A ? I type conclusion Thus, our derived conclusion would be:
"Some citizens are men".
This is conclusion on I.
- 8. Statements:
(a) Some shoes are White.
(b) All White are Blue.
Conclusions:
I. All shoes are Blue.
II. Some shoes are Blue.
Options- A. Only I follows
- B. Only II follows
- C. Neither I nor II follows
- D. Both I and II follow Discuss
Correct Answer: Only II follows
Explanation:
First Premise is Particular Affirmative (I-type)
Second Premise is Universal Affirmative (A-type).
Some shoes are white. ? All white are blue.
I + A ? I-type of Conclusion "Some shoes are blue."
This is Conclusion II.
- 9. Statements:
Some files are numbered.
All numbers are coded.
Inferences:
Options- A. All files are coded.
- B. All codes are filed.
- C. Some files are not numbered.
- D. No numbers have codes Discuss
Correct Answer: All files are coded.
Explanation:
Both the Premises are Universal Affirmative (A-type).
All files are numbered. ? All numbers are coded.
A + A ? A-type of Conclusion "All files are coded."
This is Conclusion I.
- 10. Statements:
(a) All goats are tigers.
(b) All tigers are lions.
Conclusions:
I. All tigers are goats.
II. All lions are tigers.
III. No goat is a lion.
IV. No lion is a goat.
Options- A. Either II or III follows
- B. Either II or IV follows
- C. Either I or III follows
- D. None of the conclusions follow Discuss
Correct Answer: None of the conclusions follow
Explanation:
Both the Premises are Universal Affirmative (A-type).
All goats are tigers. ? All tigers are lions.
A + A ? A-type of Conclusion
"All goats are lions."
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