The statements below are followed by two conclusions labeled 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 flowers are fruits.
All fruits are Plants.
Conclusions:
I. All Plants are flowers.
II. Some fruits are flowers.
- ABoth Conclusions I and II follow.
- BOnly Conclusion I follows.
- COnly Conclusion II follows.
- DEither Conclusion I or II follows.
Solution & Step-by-step Explanation
Let's evaluate the relations using Venn diagrams or containment properties:
Statement 1: Flowers⊆Fruits (All flowers are inside the fruits circle).
Statement 2: Fruits⊆Plants (All fruits are inside the plants circle).
Combining these gives: Flowers⊆Fruits⊆Plants.
Now let's check the conclusions:
Conclusion I: "All Plants are flowers." This means Plants⊆Flowers. From our diagram, the outer circle (Plants) is larger than the innermost circle (Flowers). Therefore, all plants are not necessarily flowers. This conclusion does not follow.
Conclusion II: "Some fruits are flowers." Since all flowers are fruits, the region where flowers exist represents a portion of fruits that are flowers. This conclusion definitely follows.
Statement 1: Flowers⊆Fruits (All flowers are inside the fruits circle).
Statement 2: Fruits⊆Plants (All fruits are inside the plants circle).
Combining these gives: Flowers⊆Fruits⊆Plants.
Now let's check the conclusions:
Conclusion I: "All Plants are flowers." This means Plants⊆Flowers. From our diagram, the outer circle (Plants) is larger than the innermost circle (Flowers). Therefore, all plants are not necessarily flowers. This conclusion does not follow.
Conclusion II: "Some fruits are flowers." Since all flowers are fruits, the region where flowers exist represents a portion of fruits that are flowers. This conclusion definitely follows.