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 :
Step-by-step Explanation:
Let us analyze the given statements and the relationship between the terms using syllogism rules and Venn diagrams.
Given Statements:
1. All work is time (All W is T)
2. Some time is not progress (Some T is not P)
3. Only a few progress is result (Only a few P is R)
Given Conclusions:
I. Some work is not progress
II. All work is progress
Analysis of Conclusions:
Let's analyze the relationship between "work" (W) and "progress" (P):
- From statement 1, we know all work is inside time.
- From statement 2, we know some part of time is not progress. However, this does not give us a definite relation between work and progress.
- There is no direct negative or positive relation established between work and progress. Thus, any definite conclusion between work and progress like "Some work is not progress" (Conclusion I) or "All work is progress" (Conclusion II) individually cannot be considered definitely true. Both conclusions are individually false/doubtful.
Complementary Pair and Either-Or Case:
Let us check the conditions for the "either-or" case between Conclusion I and Conclusion II:
1. Both conclusions must have the same subject and predicate. Here, both conclusions have "work" as the subject and "progress" as the predicate.
2. Both conclusions must be individually invalid (doubtful/false). As determined, both I and II are individually invalid.
3. The pair of conclusions must form a complementary pair.
- "Some A is not B" (Particular Negative) and "All A is B" (Universal Affirmative) form a standard complementary pair.
- Since "work" and "progress" either have some parts not overlapping (Some work is not progress) or they overlap completely (All work is progress), one of these two possibilities must always be true. They cover all possible scenarios of relationship between work and progress.
Therefore, either conclusion I or conclusion II must follow.
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