The two statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All roads are streets.
Some streets are avenues.
Conclusions:
I. Some roads are avenues.
II. All avenues are roads.
- ABoth conclusions I and II follow
- BNeither conclusion I nor II follows
- COnly conclusion I follows
- DOnly conclusion II follows
Solution & Step-by-step Explanation
Let's analyze the connections using Venn diagrams:
Statement 1: "All roads are streets." This means the circle representing 'Roads' is completely inside the circle for 'Streets'.
Statement 2: "Some streets are avenues." This means the circle for 'Avenues' intersects with 'Streets'. However, this intersection does not necessarily have to touch or overlap with the 'Roads' circle.
Now let's examine the conclusions:
Conclusion I: "Some roads are avenues." Since the 'Avenues' circle may or may not intersect with 'Roads', this is a possibility but not a definite conclusion. Thus, it does not logically follow.
Conclusion II: "All avenues are roads." This is clearly incorrect since there is no statement ensuring all avenues belong to roads.
Therefore, neither conclusion I nor II follows.
Statement 1: "All roads are streets." This means the circle representing 'Roads' is completely inside the circle for 'Streets'.
Statement 2: "Some streets are avenues." This means the circle for 'Avenues' intersects with 'Streets'. However, this intersection does not necessarily have to touch or overlap with the 'Roads' circle.
Now let's examine the conclusions:
Conclusion I: "Some roads are avenues." Since the 'Avenues' circle may or may not intersect with 'Roads', this is a possibility but not a definite conclusion. Thus, it does not logically follow.
Conclusion II: "All avenues are roads." This is clearly incorrect since there is no statement ensuring all avenues belong to roads.
Therefore, neither conclusion I nor II follows.