Directions (86-89): In each of the questions below some statements are given followed by two conclusions. 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:
All work is time
Some time is not progress
Only a few progress is result
Conclusions:
I. Some work is not progress
II. All work is progress
Correct Answer :
If either conclusion I or II follow
Solution :
To determine which of the conclusions logically follow from the given statements, let us analyze the relationships step-by-step:
Step 1: Analyze the Statements
1. All work is time: This means the entire set of "work" lies inside the set of "time".
2. Some time is not progress: There is at least some portion of "time" that does not overlap with "progress".
3. Only a few progress is result: This means some "progress" is "result", and some "progress" is definitely not "result".
Step 2: Analyze the Conclusions
- Conclusion I: "Some work is not progress"
Since there is no direct negative relationship defined between "work" and "progress", we cannot definitely say that some work is not progress. Thus, this conclusion does not follow individually as a definite case.
- Conclusion II: "All work is progress"
Similarly, we do not have information to assert that all work is progress. Thus, this conclusion also does not follow individually as a definite case.
Step 3: Check for Either-Or (Complementary Pairs)
An "either-or" case exists between two conclusions when they meet the following conditions:
1. Both conclusions must have the same subject and predicate. Here, both contain "work" and "progress".
2. Both conclusions must be individually false or doubtful. Here, both I and II do not follow individually.
3. The pair of conclusions must form a complementary pair. The combination of "All A are B" and "Some A are not B" forms a standard complementary pair.
Since one of these two statements must logically be true at any given time (either all work is progress, or at least some work is not progress), they form an either-or relation.
Therefore, either conclusion I or II follows.
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