Syllogism Basics Part 4

How to rearrange the three statement: 

In this, you have to first look at the conclusion and if the conclusion doesn't directly follows then try to make the rearrangement if possible to come to the conclusion.

Must read - Syllogism Shortcut Tricks

Example 1

Statement: a. All Chairs are Tables.
b. All Tables are Tools.
c. All Tools are Cupboard

Conclusion: I. All Chairs are Cupboard
II. Some Cupboard are Tables
III. Some Cupboard are Chairs

Explanation of 1st Conclusion

Step 1: All Chairs are Tables

All Tables are Tools
All Tools are Cupboard
Apply the Cancellation method
Step 2:  All Chairs are Cupboard 

So, the conclusion one follows

Explanation of 2nd Conclusion

Step 1:  All Tables are Tools 

All Tools are Cupboard
Apply the Cancellation method 

Step 2:  All Tables are Cupboard 

Step 3:  A per the rule of possible conclusion of single statement
Some Cupboard are Table
So, the conclusion two follows

Explanation of 3rd Conclusion

Step 1:  All Chairs are Tables 

All Tables are Tools
All Tools are Cupboard
Apply the Cancellation method 

Step 2:  All Chairs are Cupboard 

Step 3: A per the rule of possible conclusion of single statement
Some Cupboard are Chairs
So, the conclusion three follows

Example 2

Statement: a. NO Pen is Pencil.
b. All Pencil is Book.
c. Some Book is Eraser.

Conclusion: I. Some Eraser is Pencil.
II. No Pencil is Pen.
III. Some Book is not Pen.

Explanation of 1st Conclusion

Step 1: All Pencil is Book 

Some Book is Eraser.
As per rule
All + Some = No Conclusion
So, there is no conclusion between all and some. That is why conclusion 1 doesn't follow.

Explanation of 2nd Conclusion

Step 1: NO Pen is Pencil 

Step 2: As per rule of Possible Conclusion of a single statement 

No Pencil is Pen
So, the conclusion two follows.

Explanation of 3rd Conclusion

Step 1: NO Pen is Pencil 

All Pencil is Book
Step 2: No + All = some not (reversed) 

Some Book is not Pen.
So, the conclusion three follows.

Example 3

Statement:
a. NO Computer is Pen drive.
b. All Laptops are Computer.
c. All Phones are Laptops.

Conclusion:
I. Some Phones are Computer.
II. No Laptops are Pen drive.
III. Some Laptops are not Phones.
Explanation of 1st Conclusion

Step 1: All Phones are Laptops. 

All Laptops are Computer.
Apply the cancellation method.
Step 2: All Phones are Computer 

Step 3: Possible Conclusion of Single Statement, 

Some Phones are Computer.
So, the conclusion one follows.

Explanation of 2nd Conclusion

Step 1: All Laptops are Computer. 

NO Computer is Pen drive.
Step 2: All + No = NO 

No Laptops are Pen drive.
So, the conclusion two follows.

Explanation of 3rd Conclusion

Step1: All Phones are Laptops. 

A possible conclusion of single statement,
Some Phones are Laptops
Step 2: Some Phones are Laptops 

All Laptops are Computer.
A possible conclusion of double statement.
Some Phones are Computer
So, the conclusion 3rd doesn't follow.

Example 4

Statement All Fans are Tub lights
All Tub lights are CFL
All CFL are LEDs

Conclusion I. All CFL being Fans is a possibility.
II. All Fans being a LEDs is a possibility
Explanation of 1st Conclusion

Step 1: All Fans are Tub lights
All Tub lights are CFL
Apply the cancellation method.
Step 2: All Fans are CFLs 

Step 3: As per the rule of Possibility conclusion
All CFL being Fans is a possibility.
So, the conclusion 1st follow.

Explanation of 2nd Conclusion

Step 1: All Fans are Tub lights 

All Tub lights are CFL
All CFL are LEDs
Apply the cancellation method.
Step 2: All Fans are LEDs 

Step 3: As per the rule if possible conclusion of single statement 

Some Fans are LEDs
Step 4: As per the rule of possibility conclusion of single statement 

All Fans being a LEDs is a possibility
So, the conclusion 2nd follow.

Example 5

Statement Some Fruits are Vegetables
Some Vegetables are Cereals.

Conclusion I. Some Fruits are Cereals
II. Some Fruits being cereals is a possibility.

Explanation of 1st Conclusion

As per the rule of syllogism,
Some + Some = No Conclusion
So, Conclusion one doesn’t follow.

Explanation of 2nd Conclusion

As per the rule of possibility,
When there is no relationship found between the statements, there is always a possibility.
So, Conclusion to follow.