Question Details

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?

Options

Both conclusions I and II follow

Only conclusion II follows

Only conclusion I follows

Neither conclusion I nor II follows

Either conclusion I or II follows

Show Answer

Correct Answer :

Option A

Both conclusions I and II follow

Solution :

The correct option is Both conclusions I and II follow.

Let us break down each statement and analyze the given conclusions step-by-step.

Step 1: Understanding the Given Statements
1. "Only a few Football is Cricket": The phrase "Only a few" indicates a definite positive and a definite negative relation together:
- Some Football is Cricket.
- Some Football is NOT Cricket.
This places a restriction on Football, meaning Football can never be completely inside Cricket. However, it does not restrict Cricket from being entirely inside Football.
2. "Some Cricket is Tennis": A basic intersection exists between the sets of Cricket and Tennis.
3. "Mostly Tennis is Badminton": In syllogism rules, "Mostly" is treated as "Some". Therefore, this statement means "Some Tennis is Badminton".

Step 2: Evaluating Conclusion I
Conclusion I: All Cricket can be Football.
- The statement "Only a few Football is Cricket" ensures that Football cannot be fully contained within Cricket.
- However, Cricket can easily sit completely inside Football while still leaving a part of Football outside of Cricket. Thus, the possibility of all Cricket being Football is entirely valid.
- Hence, Conclusion I follows.

Step 3: Evaluating Conclusion II
Conclusion II: Some Badminton can be Football.
- No definite negative relation or boundary is given between Badminton and Football.
- When two terms have no direct negative constraint between them, a possibility ("can be") between them is always logically true.
- Hence, Conclusion II follows.

Since both Conclusion I and Conclusion II logically follow, the correct option is Both conclusions I and II follow.