In each of the questions below three 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 from the given statements disregarding commonly known facts.
Statements: Only a few Copy is Pen
Only a few Pen is Stationery
No Stationery is Book
Conclusions: I. All Stationery being Copy is a possibility
II. No Copy is Book
III. Some Copy is Book
Correct Answer :
Only I and either II or III follow
Solution :
To determine which conclusions logically follow from the given statements, let us analyze the statements step-by-step using standard Venn diagram / logical deduction rules.
Given Statements:
1. Only a few Copy is Pen: This means "Some Copy is Pen" and "Some Copy is not Pen".
2. Only a few Pen is Stationery: This means "Some Pen is Stationery" and "Some Pen is not Stationery".
3. No Stationery is Book: There is zero overlap between the sets Stationery and Book.
Analysis of Conclusions:
Conclusion I: All Stationery being Copy is a possibility
There is no direct negative restriction given between Stationery and Copy. We know "Only a few Copy is Pen" and "Only a few Pen is Stationery", but nothing restricts the set of Stationery from being completely inside Copy. Since there is no contradiction created, this possibility is true.
Therefore, Conclusion I follows.
Conclusions II & III:
II. No Copy is Book
III. Some Copy is Book
Let us evaluate these two together:
Neither "No Copy is Book" nor "Some Copy is Book" is definitely true on its own because there is no direct relationship specified between Copy and Book in the statements. Copy and Book may or may not overlap.
However, the two statements form a complementary pair:
- They share the exact same elements (Copy and Book).
- One is a negative statement (No Copy is Book) and the other is a particular positive statement (Some Copy is Book).
- Either Copy and Book have no elements in common, or they share at least one element. One of these two states must logically hold true.
Therefore, Either conclusion II or conclusion III follows.
Final Conclusion:
Combining our findings, Conclusion I definitely follows, and between II and III, either II or III follows.
Thus, the correct answer is Only I and either II or III follow.
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