In the question below are given some statements followed by some conclusions based on those statements. Take 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 conclusions logically follows from the given statements. Statement : I. All A are B. II. No B is D. III. Some D are G. Conclusion : I. No A is D. II. Some G are not B. III. Some A are not G.
Both conclusions I and II follow
Understanding the Syllogism Statements
The question provides two statements and asks us to determine which of the given conclusions logically follow from these statements. We must assume the statements are true, even if they don't match real-world facts. This type of problem is based on logical deduction.
Let's break down the given statements:
- Statement I: All A are B.
- Statement II: No B is D.
- Statement III: Some D are G.
And the conclusions to evaluate are:
- Conclusion I: No A is D.
- Conclusion II: Some G are not B.
- Conclusion III: Some A are not G.
Analyzing the Conclusions Based on Statements
Analysis of Conclusion I: No A is D
We have Statement I: All A are B, and Statement II: No B is D.
If all A are inside B, and B has no overlap with D, then it logically follows that A cannot have any overlap with D either. Everything that is A is also B. Since nothing that is B is D, nothing that is A can be D.
Think of it like this: If all students are people, and no people are cats, then no students are cats. This is a direct logical deduction.
Therefore, Conclusion I, "No A is D", logically follows from the given statements.
Analysis of Conclusion II: Some G are not B
We have Statement II: No B is D, and Statement III: Some D are G.
Statement III tells us that there is at least one element (or a part of the set G) that is also in set D. Let's call this overlap region between D and G as D&G.
Statement II tells us that there is absolutely no overlap between set B and set D. This means the entire set D is separate from set B.
Since the region D&G is part of D, and the entire set D is separate from B, it means the region D&G must also be separate from B.
Thus, the part of G that is in D (which exists according to Statement III) is not in B. This means "Some G are not B".
Therefore, Conclusion II, "Some G are not B", logically follows from the given statements.
Analysis of Conclusion III: Some A are not G
We have statements connecting A to B, B to D, and D to G.
We know: All A are B, No B is D, Some D are G.
From Statement I and II, we deduced No A is D. This means A and D are completely separate.
Statement III says Some D are G. This means D and G overlap.
We need to determine if "Some A are not G" necessarily follows. We know A is separate from D. G overlaps with D. G might also overlap with A, or it might not. The statements do not provide enough information to establish a definite relationship between A and G.
Consider a scenario where set G is large enough to include all of A, in addition to overlapping with D. In this scenario, "All A are G" would be true, and "Some A are not G" would be false. Since it's possible for "Some A are not G" to be false while the statements are true, Conclusion III does not necessarily follow.
Therefore, Conclusion III, "Some A are not G", does not logically follow from the given statements.
Summary of Conclusions
Based on our analysis:
- Conclusion I (No A is D) - Follows.
- Conclusion II (Some G are not B) - Follows.
- Conclusion III (Some A are not G) - Does not follow.
Thus, both conclusions I and II logically follow from the given statements.
Important Questions from Statements and Conclusions
In the following question below are given some statements followed by some conclusions based on those statements. 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. All A are B.
II. Some B are C.
Conclusions:
I. Some A are C.
II. Some A are not C.
III. Some A are B.
In the question one statement is given, followed by two conclusions, I and II. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement : 55% of Manisha's office colleagues went to watch the movie.
Conclusion I : Manisha went to watch the movie.
Conclusion II : Manisha did not go to watch the movie.
In the question two statements are given, followed by two conclusions, I and II. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement 1 : All schools are books.
Statement 2 : No books are papers.
Conclusion I : No schools are books.
Conclusion II : Some books are schools.
In the question below are given some statements followed by some conclusions based on those statements. Take the given statements to be true even if they seem to be different from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements.
Statements:
I. Some P are Q.
II. All P are N.
Conclusion:
I. All Q are N.
II. Some P are not Q.
In the question below are given some statements followed by some conclusions based on those statements. Take the given statements to be true even if they seem to be different from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements.
Statements:
I. Some P are T.
II. Some T are S.
III. No J is P.
Conclusion:
I. Some S are not J.
II. Some T are not J.
III. Some J are not T.
