Directions: In the following question, three statements are given followed by two conclusions. Consider the given statements to be true even if they contradict generally known facts. Analyze the conclusions and determine which of them logically follow from the statements.

Statements:
Only a few Football is Cricket.
Some Cricket is Tennis.
Mostly Tennis is Badminton.
Conclusions:
I. All Cricket can be Football.
II. Some Badminton can be Football.

Which of the conclusions logically follow(s) from the given statements?

The correct option is Both conclusions I and II follow.

Step-by-step Explanation:

Let us analyze the given statements step-by-step:

1. Statement 1: "Only a few Football is Cricket"
The phrase "Only a few" implies both positive and negative definite statements: "Some Football is Cricket" and "Some Football is not Cricket". This means Football can never completely belong to Cricket, but there is no restriction stopping all Cricket from being inside Football. Therefore, it is possible for all Cricket to be Football.

2. Statement 2: "Some Cricket is Tennis"
This indicates a basic intersection between the set of Cricket and the set of Tennis.

3. Statement 3: "Mostly Tennis is Badminton"
In syllogisms, the term "Mostly" is treated as "Some". Therefore, this statement translates to "Some Tennis is Badminton".

Now, let us evaluate the conclusions:

Conclusion I: "All Cricket can be Football"
Since "Only a few Football is Cricket" restricts Football from being entirely inside Cricket, but does not restrict Cricket from being entirely inside Football, the possibility of all Cricket being Football holds true. Thus, Conclusion I follows.

Conclusion II: "Some Badminton can be Football"
There is no negative relation specified between Badminton and Football. In the absence of any definite negative statement, any possibility between unrelated entities is true. Thus, Conclusion II follows.

Therefore, both conclusions I and II follow.