Two statements are given followed by three conclusions numbered I, II, and III. 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 utensils are spoons. All bowls are spoons.
Conclusions:
I. No utensil is a bowl.
II. Some utensils are bowls.
III. No spoon is a utensil.
Only conclusion I follows
Step 1: Let's analyze the statements: - The first statement says ``All utensils are spoons." This means every utensil is a spoon, but it doesn’t necessarily mean that all spoons are utensils. - The second statement says ``All bowls are spoons." This means every bowl is a spoon, but it doesn’t necessarily mean that all spoons are bowls.
Step 2: Now let's evaluate the conclusions:
- Conclusion I: ``No utensil is a bowl." This is incorrect, because it’s possible for some utensils to be bowls, as both are types of spoons.
- Conclusion II: ``Some utensils are bowls." This is also possible, as both utensils and bowls are categorized under spoons.
- Conclusion III: ``No spoon is a utensil." This is false, as all utensils are spoons.
Thus, conclusion I or II can follow, but conclusion III does not follow.
Thus, the correct answer is option (C) Either conclusion I or II follows.
Statement: All flowers are beautiful. Some beautiful things are fragile.
Conclusion I: Some flowers are fragile.
Conclusion II: All beautiful things are flowers.