Two statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All gardens are play-grounds
No play-ground is house.
Conclusions:
I. Some gardens are houses.
II. Some play-grounds are gardens.
- ABoth conclusion I and II follow
- BOnly Conclusion I follows
- CNeither Conclusion I nor II follows
- DOnly Conclusion II follows
Solution & Step-by-step Explanation
Let's analyze the statements using Venn diagram logic:
All gardens are play-grounds: This means the circle representing 'gardens' is completely inside the circle for 'play-grounds'.
No play-ground is house: This means the circle for 'play-grounds' and the circle for 'houses' have no intersection.
Now let's evaluate the conclusions:
Conclusion I: Some gardens are houses. Since all gardens are inside play-grounds, and no play-ground can be a house, no garden can ever be a house. Therefore, Conclusion I does not follow.
Conclusion II: Some play-grounds are gardens. Since the entire 'gardens' circle lies inside 'play-grounds', the overlapping region ensures that some part of play-grounds is definitely gardens. Therefore, Conclusion II follows.
All gardens are play-grounds: This means the circle representing 'gardens' is completely inside the circle for 'play-grounds'.
No play-ground is house: This means the circle for 'play-grounds' and the circle for 'houses' have no intersection.
Now let's evaluate the conclusions:
Conclusion I: Some gardens are houses. Since all gardens are inside play-grounds, and no play-ground can be a house, no garden can ever be a house. Therefore, Conclusion I does not follow.
Conclusion II: Some play-grounds are gardens. Since the entire 'gardens' circle lies inside 'play-grounds', the overlapping region ensures that some part of play-grounds is definitely gardens. Therefore, Conclusion II follows.