In each question below, some statements are given followed by two conclusions numbered I and II. 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. Give answer -
Statements: Only a few profit is notice
Some notice is expenditure
All expenditure is subsidy
Conclusions:
I. Some notice is subsidy
II. No profit is expenditure
Correct Answer :
If only conclusion I follows
Solution :
Correct Answer: If only conclusion I follows
Let us analyze the given statements and conclusions step-by-step using Venn diagram representation.
Step 1: Analyze the Statements
1. "Only a few profit is notice": This statement implies two things:
- Some profit is notice (there is an intersection between 'profit' and 'notice').
- Some profit is NOT notice (a portion of 'profit' must remain outside of 'notice').
2. "Some notice is expenditure": This means there is an intersection between the circle for 'notice' and the circle for 'expenditure'.
3. "All expenditure is subsidy": This means the entire circle of 'expenditure' is completely contained within the circle of 'subsidy'.
Step 2: Evaluate Conclusion I ("Some notice is subsidy")
- From statement 2, we know that "Some notice is expenditure". This means there is a common region between 'notice' and 'expenditure'.
- From statement 3, we know that "All expenditure is subsidy", which means any region belonging to 'expenditure' must also belong to 'subsidy'.
- Since the intersecting part of 'notice' and 'expenditure' is entirely inside 'subsidy', this intersecting region must also be shared between 'notice' and 'subsidy'.
- Therefore, there is definitely an intersection between 'notice' and 'subsidy'. Thus, Conclusion I logically follows.
Step 3: Evaluate Conclusion II ("No profit is expenditure")
- The statements do not define any direct relation between 'profit' and 'expenditure'.
- While we can draw a Venn diagram where 'profit' and 'expenditure' do not intersect (making the conclusion seem true in that specific diagram), we can also draw a valid Venn diagram where 'profit' and 'expenditure' do intersect because there is no restriction preventing them from overlapping.
- Since "No profit is expenditure" is not true in all possible scenarios, it is not a definite conclusion. Thus, Conclusion II does not follow.
Conclusion:
Only conclusion I follows from the given statements.
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