In each question below, some statements are given followed by some conclusions. You have to assume everything in the statements to be true even if they seem to be at variance with commonly known facts. Now, decide which of the two given conclusions logically follow from the statements, disregarding commonly known facts.
Statements:
Only travel are planet.
Some crow are travel.
All crow are silver.
Conclusions:
I. Some planet being silver is a possibility.
II. All travel can never be crow.
Correct Answer :
Only II follows
Solution :
To determine which of the conclusions logically follow from the given statements, we can analyze the statements step-by-step using Venn diagrams and logical deductions.
Step 1: Analyze the Statements
1. "Only travel are planet."
This is an exclusive statement. In formal logic, "Only A are B" is equivalent to "All B are A", with an additional constraint: no element outside of A can ever be B. Thus, "Only travel are planet" means:
⇒ All planet are travel.
⇒ Crucially, planet cannot belong to or intersect with any other category except travel. Specifically, planet cannot be crow, and planet cannot be silver.
2. "Some crow are travel."
This means there is an intersection between the set of "crow" and the set of "travel".
3. "All crow are silver."
This means the entire set of "crow" is contained within the set of "silver". Since some crow are travel, it also means that some silver are travel.
Step 2: Evaluate Conclusion I
Conclusion I: "Some planet being silver is a possibility."
From Statement 1 ("Only travel are planet"), planet can only belong to travel and cannot overlap with any other group like silver. Therefore, it is impossible for any planet to be silver. Thus, Conclusion I does not follow.
Step 3: Evaluate Conclusion II
Conclusion II: "All travel can never be crow."
Let us check if it is possible for all travel to be crow.
If all travel were crow, then since "All planet are travel" (from Statement 1), all planet would also have to be crow.
However, because of the "Only travel are planet" rule, planet cannot overlap with any category other than travel. Since planet cannot be crow, all travel can never be crow (as there must always be a part of travel, containing planet, that remains outside of crow).
Therefore, the statement "All travel can never be crow" is definitely true. Thus, Conclusion II logically follows.
Conclusion
Only Conclusion II follows.
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