Read the given statements 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 statements.
Statements:
All students are enthusiasts.
No enthusiast is a candidate.
All leaders are students.
Conclusions:
I. No leader is a candidate.
II. No student is a candidate.
III. No candidate is an enthusiast.
- AAll conclusions I, II and III follow.
- BOnly conclusions I and II follow.
- COnly conclusions II and III follow.
- DOnly conclusions I and III follow.
Solution & Step-by-step Explanation
Let's analyze the statements using Venn diagrams:
"All students are enthusiasts" → The set of Students is entirely inside the set of Enthusiasts.
"All leaders are students" → The set of Leaders is entirely inside the set of Students. Thus, Leaders are also entirely inside Enthusiasts.
"No enthusiast is a candidate" → The set of Enthusiasts and the set of Candidates have absolutely no overlap.
Now let's evaluate the conclusions:
Conclusion I: "No leader is a candidate." Since all leaders are inside enthusiasts, and no enthusiast can touch candidates, leaders can never touch candidates. This is true.
Conclusion II: "No student is a candidate." Since all students are inside enthusiasts, and enthusiasts are separate from candidates, students can never touch candidates. This is true.
Conclusion III: "No candidate is an enthusiast." This is the direct converse statement of "No enthusiast is a candidate". This is true.
Therefore, all conclusions I, II, and III follow.
"All students are enthusiasts" → The set of Students is entirely inside the set of Enthusiasts.
"All leaders are students" → The set of Leaders is entirely inside the set of Students. Thus, Leaders are also entirely inside Enthusiasts.
"No enthusiast is a candidate" → The set of Enthusiasts and the set of Candidates have absolutely no overlap.
Now let's evaluate the conclusions:
Conclusion I: "No leader is a candidate." Since all leaders are inside enthusiasts, and no enthusiast can touch candidates, leaders can never touch candidates. This is true.
Conclusion II: "No student is a candidate." Since all students are inside enthusiasts, and enthusiasts are separate from candidates, students can never touch candidates. This is true.
Conclusion III: "No candidate is an enthusiast." This is the direct converse statement of "No enthusiast is a candidate". This is true.
Therefore, all conclusions I, II, and III follow.