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In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some pen are black.
II. Some pen are blue.
III. No black is red.
Conclusions:
I. No pen is red.
II. Some blue are black.
III. Some black are pens.
  • a)
    Only I
  • b)
    Only II
  • c)
    Only III
  • d)
    Only II and III
Correct answer is option 'C'. Can you explain this answer?
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In the following question below are given some statements followed by ...
Given statements:
I. Some pen are black.
II. Some pen are blue.
III. No black is red.

Conclusions:
I. No pen is red.
II. Some blue are black.
III. Some black are pens.

Explanation:

Conclusion I: No pen is red.
This conclusion can be derived from the given statement III, which states that "No black is red". Since some pens are black and there are no red pens mentioned in the statements, we can conclude that no pen is red. Therefore, conclusion I logically follows.

Conclusion II: Some blue are black.
This conclusion cannot be directly derived from the given statements. Although it is mentioned that some pens are black and some pens are blue, there is no specific information given about the relationship between black and blue pens. Therefore, conclusion II does not logically follow.

Conclusion III: Some black are pens.
This conclusion is already mentioned in the given statements. Statement I states that "Some pen are black", which implies that there are pens that are black. Therefore, conclusion III logically follows.

Conclusion Summary:
- Conclusion I: No pen is red. (Logically follows)
- Conclusion II: Some blue are black. (Does not logically follow)
- Conclusion III: Some black are pens. (Logically follows)

Therefore, the correct answer is option 'C' - Only III.
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