Statements : All fruits are vegetables. All pens are vegetables. All vegetables are rains. Conclusions : I. All fruits are rains. II. All pens are rains. III. Some rains are vegetables.

The correct answer is: C. Only II and III follow

The first statement is “All fruits are vegetables.” This means that every member of the set of fruits is also a member of the set of vegetables. The second statement is “All pens are vegetables.” This means that every member of the set of pens is also a member of the set of vegetables. The third statement is “All vegetables are rains.” This means that every member of the set of vegetables is also a member of the set of rains.

The first conclusion is “All fruits are rains.” This conclusion does not follow from the premises. The premises only say that every member of the set of fruits is also a member of the set of vegetables. They do not say anything about whether or not every member of the set of vegetables is also a member of the set of rains. Therefore, we cannot conclude that all fruits are rains.

The second conclusion is “All pens are rains.” This conclusion does follow from the premises. The premises say that every member of the set of pens is also a member of the set of vegetables. And the premises also say that every member of the set of vegetables is also a member of the set of rains. Therefore, we can conclude that all pens are rains.

The third conclusion is “Some rains are vegetables.” This conclusion does follow from the premises. The premises say that every member of the set of vegetables is also a member of the set of rains. Therefore, we can conclude that there is at least one rain that is also a vegetable.

In conclusion, only the second and third conclusions follow from the premises.