Syllogism problems
- 1. Statements
1. Authors are learned people.
2. Some doctors are authors.
Conclusions
I. Some doctors are learned people.
II. Some learned people are doctors.
Options- A. Both I and II are implicit.
- B. Neither I nor II is implicit.
- C. Only I is implicit.
- D. Only II is implicit. Discuss
Correct Answer: Both I and II are implicit.
Explanation:
First Premise is Universal Affirmative (A - type).
Second Premise is Particular Affirmative (I - type).
Some doctors are authors. ? (All) Authors are learned people
I + A ? I - type of Conclusion "Some doctors are learned people."
This is Conclusion I. Conclusion II is the Converse of it.
- 2. Statements:
I. Some leaves are apples.
II. No apple is an egg.
Conclusions:
I. All apples are leaves.
II. Some eggs are leaves.
III. Some leaves are not eggs.
IV. All eggs are leaves.
Options- A. Only III follows
- B. None follows
- C. Either II or III follow
- D. All follow Discuss
Correct Answer: Only III follows
Explanation:
First premise is Particular Affirmative (I-type).
Second Premise is Universal Negative (E-type).
Some leaves are apples. ? No apple is an egg.
I + E ? O-type of Conclusion "Some leaves are not eggs".
This is Conclusion III.
- 3. Statements:
Some spoons are cups.
Some cups are bottles.
All bottles are mugs.
Conclusions:
I. Some mugs are cups.
II. Some cups are bottles.
III. Some spoons are mugs.
Options- A. Either I or II and III follows
- B. Only II follows
- C. Only I and II follows
- D. All follow Discuss
Correct Answer: Only I and II follows
Explanation:
First and second premises are particular Affirmative (I? type).
Third Premises is Universal Affirmative (A?type).
Some cups are bottles. ? All bottles are mugs.
I + A ? I?type of Conclusion "Some cups are mugs."
Conclusion I is the Converse of it.
Conclusion II is the same as that of second premise.
- 4. Statements:
1. All apples are oranges.
2. Some oranges are papayas.
Conclusions:
I. Some apples are papayas.
II. Some papayas are apples.
Options- A. Only Conclusion II follows
- B. Both Conclusions I and II follow
- C. Neither Conclusion I nor II follows
- D. Only Conclusion I follows Discuss
Correct Answer: Neither Conclusion I nor II follows
Explanation:
First Premise is Universal Affirmative (A?type).
Second Premise is Particular Affirmative (I?type).
All apples are oranges. ? Some oranges are papayas.
A+I ? No Conclusion
- 5. Statements:
(i) Some papers are pens.
(ii) All the pencils are pens.
Conclusions:
I. Some pens are pencils.
II. Some pens are papers.
Options- A. Only II Conclusion follows
- B. Either I or II follows
- C. Both I and II follow
- D. Only I Conclusion follows Discuss
Correct Answer: Both I and II follow
Explanation:
First Premise is the Particular Affirmative (I-type).
Second Premise is the Universal Affirmative (A-type).
All the pencils are pens. ? Some pens are papers.
A + I ? No Conclusion
Conclusion I is the Converse of the second Premise.
Conclusion II is the Converse of the first Premise.
- 6. Statements:
1. Some teachers are followers.
2. Some followers are famous.
Conclusions:
I. Some teachers are famous.
II. Some followers are teachers.
Options- A. Only Conclusion I follows
- B. Only Conclusion II follows
- C. Both Conclusions I and II follow
- D. Neither Conclusion I nor II follows Discuss
Correct Answer: Only Conclusion II follows
Explanation:
Both the Premises are Particular Affirmative (I-type).
No Conclusion follows from the two Particular Premises.
Conclusion II is the Converse of the first Premise.
- 7. Statements:
1. All trees are leaves.
2. Some fruits are leaves.
Conclusions:
I. Some fruits are trees.
II. Some leaves are trees.
Options- A. Only Conclusion I follows
- B. Only Conclusion II follow
- C. Both Conclusions I and II follow
- D. Neither Conclusion I nor II follows Discuss
Correct Answer: Only Conclusion II follow
Explanation:
First Premise is Universal Affirmative (A-type).
Second Premise is Particular Affirmative (I-type).
All trees are leaves. ? Some leaves are fruits.
A + I ? No Conclusion
Conclusion II is Converse of the first Premise.
- 8. Statement:
All goats are flowers.
No flower is branch.
Some branches are roots.
Conclusions:
I. Some roots are goats.
II. No roots are goat.
Options- A. if conclusion I follow
- B. if conclusion II follows
- C. if either conclusion I or II follows
- D. if neither conclusion I nor II follows Discuss
Correct Answer: if either conclusion I or II follows
Explanation:
All goats are flowers + No flower is branch = 1 + A = E = E = No goat is branch + Some branches are roots = E + 1 = 0* = Some roots are not goats. Hence neither I nor II definitely follows However, since the two from a complementary I - E pair, either of two must follow.
- 9. Statement:
All pots are rings.
All bangles are rings.
All rings are paints.
Conclusions:
I. Some paints are pots.
II. Some bangles are paints.
Options- A. if conclusion I follow
- B. if conclusion II follows
- C. if either conclusion I or II follows
- D. if neither conclusion I nor II follows Discuss
Correct Answer:
Explanation:
All pots are rings + All rings are paints = A + A = A = All pots are paints ? conversion ? Some paints are pots (I) Hence I follows. All bangles are rings + All rings are paints = A + A = A = All bangles are paints ? implication ? Some bangles are paints (I) Hence II follows.
- 10. Statement:
All pictures are paintings.
All paintings are photographs.
Some photographs are designs.
Conclusions:
I. Some paintings are designs.
II. Some photographs are movies.
Options- A. if conclusion I follow
- B. if conclusion II follows
- C. if either conclusion I or II follows
- D. if neither conclusion I nor II follows Discuss
Correct Answer: if neither conclusion I nor II follows
Explanation:
All paintings are photographs + Some photographs are designs = A + I = No conclusion Hence I does not follow. Some photographs are designs + Some designs are movies = I + I = No conclusion Hence II does not follows.
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