Directions: In the question below, three statements are given followed by two conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow from the given statements.
Statements:
Only a few novels are hardcovers
All hardcovers are publications
No publication is audio
Conclusions:
I. Some novels are not audio
II. All hardcovers being novels is a possibility
Correct Answer :
Both conclusions I and II follow
Solution :
The correct answer is Both conclusions I and II follow.
Step-by-Step Explanation:
1. Analyze the given statements:
• Statement 1: "Only a few novels are hardcovers"
This statement implies two distinct conditions:
- Some novels are hardcovers
- Some novels are not hardcovers
• Statement 2: "All hardcovers are publications"
This means the entire set of Hardcovers is contained within the set of Publications.
• Statement 3: "No publication is audio"
This means there is no overlap between the set of Publications and the set of Audio.
2. Evaluate Conclusion I: "Some novels are not audio"
From Statement 1, we know that there are some novels that are hardcovers.
From Statement 2, all hardcovers are publications. Therefore, those novels that are hardcovers are also publications.
From Statement 3, no publication is audio. Since those specific novels are publications, they cannot be audio.
Thus, at least those novels which are hardcovers are definitely not audio. Hence, Conclusion I logically follows.
3. Evaluate Conclusion II: "All hardcovers being novels is a possibility"
The statement "Only a few novels are hardcovers" restricts the set of novels (meaning not all novels can be hardcovers, so some novels must remain outside of hardcovers). However, it does not prevent all hardcovers from being included inside the set of novels, provided the set of novels is larger than the set of hardcovers.
Therefore, a scenario in which all hardcovers are novels does not violate any given statement and is a valid possibility. Hence, Conclusion II logically follows.
Conclusion:
Since both Conclusion I and Conclusion II logically follow from the given statements, the correct answer is Both conclusions I and II follow.
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