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:
Some mugs are rugs.
All tugs are mugs.
Conclusions:
I. Some rugs are mugs.
II. Some mugs are tugs.
III. No rug is a mug.
- ABoth conclusions II and III follow.
- BBoth conclusions I and III follow.
- CAll conclusions I, II and III follow.
- DBoth conclusions I and II follow.
Solution & Step-by-step Explanation
Let's evaluate each conclusion systematically:
Conclusion I: "Some rugs are mugs." The first statement clearly tells us "Some mugs are rugs." Since the relation "some" is symmetrical, "Some rugs are mugs" is definitely true. Thus, Conclusion I follows.
Conclusion II: "Some mugs are tugs." The second statement tells us "All tugs are mugs." This implies that the entire set of tugs resides inside the set of mugs, meaning there are definitely some mugs that are tugs. Thus, Conclusion II follows.
Conclusion III: "No rug is a mug." This directly contradicts Conclusion I, which we already found to be true. Thus, Conclusion III does not follow.
Therefore, both conclusions I and II follow.
Conclusion I: "Some rugs are mugs." The first statement clearly tells us "Some mugs are rugs." Since the relation "some" is symmetrical, "Some rugs are mugs" is definitely true. Thus, Conclusion I follows.
Conclusion II: "Some mugs are tugs." The second statement tells us "All tugs are mugs." This implies that the entire set of tugs resides inside the set of mugs, meaning there are definitely some mugs that are tugs. Thus, Conclusion II follows.
Conclusion III: "No rug is a mug." This directly contradicts Conclusion I, which we already found to be true. Thus, Conclusion III does not follow.
Therefore, both conclusions I and II follow.