Directions (86-89): In each of the questions below some 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 follows from the given statements disregarding commonly known facts.
Statements:
Only a few rice is wheat
All wheat is grain
No grain is flour
Conclusions:
I. Some rice is not flour
II. All wheat can be flour
Correct Answer :
If only conclusion I follow
Solution :
Let us analyze the given statements step-by-step using standard rules of syllogism and Venn diagram concepts:
Statements:
1. "Only a few rice is wheat": This statement implies two things:
- Some rice is wheat.
- Some rice is not wheat (a part of rice can never be wheat).
2. "All wheat is grain": This means the entire set of wheat is inside the set of grain.
3. "No grain is flour": This means there is no intersection (overlap) between the set of grain and the set of flour. Since all wheat is inside grain, this also implies that no wheat is flour.
Now, let us evaluate the conclusions based on these relations:
Conclusion I: "Some rice is not flour"
- From the statements, we know that "Some rice is wheat" (since only a few rice is wheat).
- We also know that "All wheat is grain" and "No grain is flour", which means that no wheat can be flour.
- Therefore, the portion of rice that is wheat can never be flour. This portion of rice constitutes "some rice".
- Thus, the conclusion "Some rice is not flour" is definitely true and logically follows.
Conclusion II: "All wheat can be flour"
- We know that "All wheat is grain" and "No grain is flour".
- This means there is a direct restriction between grain and flour, making it impossible for any wheat to overlap with flour.
- Therefore, no wheat can ever be flour. The possibility "All wheat can be flour" is completely false.
- Thus, conclusion II does not follow.
Hence, only conclusion I follows.
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