Statements:
Only a few clouds are rains
All rains are droplet
Some rains are winds
Conclusions:
I. Some winds being clouds is a possibility.
II. Some droplet is winds
III. No clouds are droplet
In each question below, some statements are given followed by three conclusions numbered I, II and III. 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.
Correct Answer :
Both I and II
Solution :
To determine which of the conclusions logically follow from the given statements, we can analyze them step-by-step using Venn diagrams and logical deduction.
First, let's break down the statements:
1. "Only a few clouds are rains": This means that some clouds are rains, and also some clouds are definitely not rains.
2. "All rains are droplet": This means the entire group of "rains" is contained within the group of "droplet".
3. "Some rains are winds": This means there is an intersection between the group of "rains" and the group of "winds".
Now, let's evaluate each conclusion:
Conclusion I: Some winds being clouds is a possibility.
From the statements, we know that "Some rains are winds" and "Only a few clouds are rains" (so some clouds are rains). The group of "winds" and the group of "clouds" both intersect with "rains", but there is no statement that prevents them from overlapping directly with each other. Therefore, it is entirely possible for some winds to be clouds. Since this is a possibility, Conclusion I is true.
Conclusion II: Some droplet is winds.
We are given that "All rains are droplet" and "Some rains are winds". Since all rains are inside the droplet group, any part of the rain group that intersects with winds must also be inside the droplet group. Therefore, the intersection between rains and winds guarantees that there is an intersection between droplets and winds. Thus, some droplets are definitely winds. Conclusion II follows logically.
Conclusion III: No clouds are droplet.
We know that "Only a few clouds are rains" (which implies some clouds are rains) and "All rains are droplet". Since some clouds are rains, and all rains are droplets, those clouds that are rains must also be droplets. Therefore, there is definitely an overlap between clouds and droplets, which contradicts the claim that "No clouds are droplet". Thus, Conclusion III does not follow.
Conclusion:
Only conclusions I and II follow logically from the given statements.
Therefore, the correct option is Both I and II.
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