Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All nodes are joints.
Some joints are bones.
All bones are cartilages.
Conclusions:
I. No node is a bone.
II. All joints are cartilages.
III. Some cartilages are nodes.
- AOnly conclusions II and III follow
- BOnly conclusion I follows
- COnly conclusions I and II follow
- DNone of the conclusions follow
Solution & Step-by-step Explanation
Let's analyze each conclusion using standard syllogism logic:
Conclusion I: "No node is a bone."
From the statements, "All nodes are joints" and "Some joints are bones". There is a possibility that nodes overlap with bones, but it is not definite. Since it's a negative statement and we cannot definitely rule out overlapping, this does not follow.
Conclusion II: "All joints are cartilages."
We only know that "Some joints are bones" and "All bones are cartilages". This guarantees only that some joints (those that are bones) are cartilages. It does not mean all joints are cartilages. Thus, this does not follow.
Conclusion III: "Some cartilages are nodes."
There is no definite connection given between nodes and cartilages. It's possible but not definite. Thus, this does not follow.
Since none of the three conclusions definitely follow, the correct option is None of the conclusions follow.
Conclusion I: "No node is a bone."
From the statements, "All nodes are joints" and "Some joints are bones". There is a possibility that nodes overlap with bones, but it is not definite. Since it's a negative statement and we cannot definitely rule out overlapping, this does not follow.
Conclusion II: "All joints are cartilages."
We only know that "Some joints are bones" and "All bones are cartilages". This guarantees only that some joints (those that are bones) are cartilages. It does not mean all joints are cartilages. Thus, this does not follow.
Conclusion III: "Some cartilages are nodes."
There is no definite connection given between nodes and cartilages. It's possible but not definite. Thus, this does not follow.
Since none of the three conclusions definitely follow, the correct option is None of the conclusions follow.