In this logical reasoning question, you are given two statements about cakes, pastries, and bread, followed by two conclusions. You must treat the statements as true, even if they seem unusual, and then decide which conclusion or conclusions logically follow. Statement I: All cakes are pastries. Statement II: Some bread are cakes. Conclusion I: No pastries are bread. Conclusion II: Some bread are pastries. Choose the option that correctly identifies which conclusion or conclusions follow.

Difficulty: Easy

Correct Answer: Only conclusion II follows

Explanation:


Introduction / Context:
This question is another example of syllogistic reasoning involving food items: cakes, pastries, and bread. The problem checks whether you can correctly trace set relations and identify which conclusions are forced by the given statements.


Given Data / Assumptions:
The following statements are treated as fully true.

  • Statement I: All cakes are pastries.
  • Statement II: Some bread are cakes.
  • Conclusion I: No pastries are bread.
  • Conclusion II: Some bread are pastries.
  • “Some” means at least one, possibly more.


Concept / Approach:
If all cakes are pastries, then the Cake set lies inside the Pastry set. If some bread are cakes, then at least some elements in the Bread set are also in the Cake set. Combining these two, those bread items must also lie inside the Pastry set. This directly suggests a connection between bread and pastries.


Step-by-Step Solution:

Step 1: From statement I, every cake is a pastry. So Cake is a subset of Pastry. Step 2: From statement II, at least one bread item is a cake. Therefore, there is at least one element in the intersection of Bread and Cake. Step 3: Because every cake is inside the Pastry set, that bread item, which is a cake, must also be a pastry. So there exists at least one object that is both bread and pastry. Step 4: Hence, “Some bread are pastries” is certainly true. This matches conclusion II. Step 5: Conclusion I states “No pastries are bread.” This would mean the Pastry and Bread sets do not overlap. We just found that there is at least one item that is both bread and pastry, so conclusion I cannot be true.


Verification / Alternative check:
Draw three sets. Place Cake inside Pastry. Mark a point where Bread and Cake intersect. Because this point is in Cake and Cake lies inside Pastry, that same point must be in Pastry as well. So there is a definite overlap between Bread and Pastry. This visually confirms that conclusion II must hold and conclusion I must fail.


Why Other Options Are Wrong:
Option A claims only conclusion I follows, which directly contradicts the set relations. Option C claims both follow, but two contradictory statements cannot both be true in standard logic. Option D says neither follows, which ignores the clear deduction that some bread are pastries.


Common Pitfalls:
Learners sometimes mentally separate bakery categories and assume that bread and pastries do not overlap. However, logical reasoning questions do not care about real life labels. You must work strictly with the relations given. Once you accept that some bread are cakes and all cakes are pastries, you must accept that some bread are pastries.


Final Answer:
The only valid conclusion is conclusion II. Therefore, the correct choice is “Only conclusion II follows.”

More Questions from Statement and Conclusion

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion