Question :
Option :
- Neither conclusion I nor II follows
- Both conclusions I and II follow
- Only conclusion II follows
- Only conclusion I follows
correct answer : b)
Solution to the Logical Reasoning Question:
We are given three statements and two conclusions. We need to determine which conclusions logically follow from the statements.
#### **Given Statements:**
1. **Statement I:** All bats are balls.
– Bat → Ball
2. **Statement II:** All balls are badmintons.
– Ball → Badminton
3. **Statement III:** All badmintons are wickets.
– Badminton → Wicket
—
#### **Conclusions to Evaluate:**
1. **Conclusion I:** All bats are wickets.
2. **Conclusion II:** Some badmintons are bats.
—
### **Step-by-Step Analysis:**
#### **1. Visual Representation (Venn Diagram):**
– From **Statement I (All bats are balls):**
The “Bat” circle is entirely inside the “Ball” circle.
– From **Statement II (All balls are badmintons):**
The “Ball” circle (which includes “Bat”) is entirely inside the “Badminton” circle.
– From **Statement III (All badmintons are wickets):**
The “Badminton” circle (which includes “Ball” and “Bat”) is entirely inside the “Wicket” circle.
**Final Hierarchy:**
Bat → Ball → Badminton → Wicket
—
#### **2. Evaluating Conclusion I: “All bats are wickets.”**
– From the hierarchy:
Bat → Ball → Badminton → Wicket
This means every bat is ultimately a wicket.
– **Verification:**
– All bats are balls (given).
– All balls are badmintons (given).
– All badmintons are wickets (given).
Thus, all bats must be wickets.
– **Result:** **Conclusion I follows.**
—
#### **3. Evaluating Conclusion II: “Some badmintons are bats.”**
– From the hierarchy:
All bats are badmintons (since Bat → Ball → Badminton).
This means the entire “Bat” set is inside the “Badminton” set.
– **Implication:**
Since “Bat” is a non-empty subset of “Badminton,” there must exist at least some badmintons that are bats.
– **Result:** **Conclusion II follows.**
—
### **Final Answer:**
Both **Conclusion I** and **Conclusion II** logically follow from the given statements.
**Correct Option:**
**2. Both conclusions I and II follow**
—
### **Key Takeaways:**
1. **Conclusion I (All bats are wickets):**
– Follows by transitive property (Bat → Ball → Badminton → Wicket).
2. **Conclusion II (Some badmintons are bats):**
– Follows because “All bats are badmintons” implies “Some badmintons are bats” (as “Bat” is a non-empty subset).
Thus, the correct choice is **Option 2**.