Read the given statement(s) and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statement(s).
Statements:
Some Queens are kings.
All kings are officers.
No officer is architect.
Conclusions:
I. Some officers are queens.
II. No king is architect.
- AEither conclusion I or II follows.
- BBoth the conclusions follow.
- COnly conclusion II follows.
- DOnly conclusion I follows.
Solution & Step-by-step Explanation
Let's analyze the statements using standard logical intersections:
Statement 1: "Some Queens are kings." → There is a mutual overlap between the set of Queens and the set of Kings.
Statement 2: "All kings are officers." → The entire set of Kings is contained inside the set of Officers. Since some Queens are Kings, those specific Queens are now automatically inside the set of Officers as well.
Statement 3: "No officer is architect." → The set of Officers and the set of Architects are completely disjoint.
Now, let's examine the conclusions:
Conclusion I: "Some officers are queens." Since the entire set of Kings is inside Officers, and some Queens are Kings, the intersection between Officers and Queens must contain those individuals. Hence, Conclusion I is true.
Conclusion II: "No king is architect." Since all Kings are inside the set of Officers, and no part of Officers can overlap with Architects, no King can ever overlap with an Architect. Hence, Conclusion II is also true.
Therefore, both conclusions I and II follow.
Statement 1: "Some Queens are kings." → There is a mutual overlap between the set of Queens and the set of Kings.
Statement 2: "All kings are officers." → The entire set of Kings is contained inside the set of Officers. Since some Queens are Kings, those specific Queens are now automatically inside the set of Officers as well.
Statement 3: "No officer is architect." → The set of Officers and the set of Architects are completely disjoint.
Now, let's examine the conclusions:
Conclusion I: "Some officers are queens." Since the entire set of Kings is inside Officers, and some Queens are Kings, the intersection between Officers and Queens must contain those individuals. Hence, Conclusion I is true.
Conclusion II: "No king is architect." Since all Kings are inside the set of Officers, and no part of Officers can overlap with Architects, no King can ever overlap with an Architect. Hence, Conclusion II is also true.
Therefore, both conclusions I and II follow.