Three 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 given conclusions logically follow(s) from the statements.
Statements:
Some fractions are marts.
No mart is a stud.
All studs are frogs.
Conclusions:
I. Some fractions are definitely not studs.
II. Some fractions are definitely not marts.
- AOnly conclusion II follows
- BEither conclusion I or II follows
- COnly conclusion I follows
- DBoth conclusions I and II follow
Solution & Step-by-step Explanation
Let's analyze the conclusions using a Venn diagram or logical deductions:
Statement 1: Some fractions are marts. (There is an intersecting area between Fractions and Marts).
Statement 2: No mart is a stud. (The sets of Marts and Studs are completely disjoint).
Statement 3: All studs are frogs.
Now evaluate the conclusions:
Conclusion I: Some fractions are definitely not studs.
The part of 'fractions' that overlaps with 'marts' cannot be 'studs' because no mart can be a stud. Since some fractions are marts, that specific portion of fractions will never be studs. Hence, this conclusion definitely follows.
Conclusion II: Some fractions are definitely not marts.
From Statement 1, we only know that "some fractions are marts." We cannot definitively conclude that the remaining fractions are not marts (it could be that all fractions are marts in a possibility). Therefore, this definite negative statement does not follow.
Thus, only conclusion I follows.
Statement 1: Some fractions are marts. (There is an intersecting area between Fractions and Marts).
Statement 2: No mart is a stud. (The sets of Marts and Studs are completely disjoint).
Statement 3: All studs are frogs.
Now evaluate the conclusions:
Conclusion I: Some fractions are definitely not studs.
The part of 'fractions' that overlaps with 'marts' cannot be 'studs' because no mart can be a stud. Since some fractions are marts, that specific portion of fractions will never be studs. Hence, this conclusion definitely follows.
Conclusion II: Some fractions are definitely not marts.
From Statement 1, we only know that "some fractions are marts." We cannot definitively conclude that the remaining fractions are not marts (it could be that all fractions are marts in a possibility). Therefore, this definite negative statement does not follow.
Thus, only conclusion I follows.