In the question, two statements are given, followed by two conclusions, I and II. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement I: No cans are jars
Statement II: All tins are cans
Conclusion I: All jars are tins
Conclusion II: No tins are jars
- AOnly conclusion I follows
- BOnly conclusion II follows
- CBoth conclusions I and II follow
- DNeither conclusion I nor conclusion II follows
Solution & Step-by-step Explanation
Let's parse the logical boundaries using set theory relationships:
Statement II says "All tins are cans". This means the set of Tins lies entirely inside the set of Cans (Tins⊆Cans).
Statement I says "No cans are jars". This means the set of Cans and the set of Jars are completely disjoint (Cans∩Jars=∅).
Since the entire set of Tins is trapped inside Cans, and Cans cannot touch Jars, it naturally implies that no element of Tins can ever touch Jars (Tins∩Jars=∅).
Now, let's analyze the conclusions:
Conclusion I: "All jars are tins" → This is false because no jar can be a tin.
Conclusion II: "No tins are jars" → This is absolutely true based on our deduction.
Therefore, only conclusion II follows.
Statement II says "All tins are cans". This means the set of Tins lies entirely inside the set of Cans (Tins⊆Cans).
Statement I says "No cans are jars". This means the set of Cans and the set of Jars are completely disjoint (Cans∩Jars=∅).
Since the entire set of Tins is trapped inside Cans, and Cans cannot touch Jars, it naturally implies that no element of Tins can ever touch Jars (Tins∩Jars=∅).
Now, let's analyze the conclusions:
Conclusion I: "All jars are tins" → This is false because no jar can be a tin.
Conclusion II: "No tins are jars" → This is absolutely true based on our deduction.
Therefore, only conclusion II follows.