Premises - Type 3: No A is B

We can represent this premise by the following Venn diagram:  

Types of Premises: Venn Diagram Representation of "No A is B".
Venn Diagram

The only definite conclusion, we have from this premise is “No B is A”.

Your Turn:

Let’s practice what we have learnt. In the questions below two statements are given and these statements are followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts.

Practice Exercise 1:

Statements: 

No burger is sandwich.

No sandwich is pizza.

Conclusions:

I. No burger is pizza.

II. Some pizzas are sandwiches.

We can draw the Venn diagram representation of the statements as shown:  

Venn Diagram Representation of Practice Exercise 1Since we are not given any relation between burgers and pizzas, there is a possibility that some pizzas might be burgers as well. We have represented this possibility with a dotted circle in the Venn diagram.

Now let’s see which of the conclusions are correct:

I. No burger is pizza.

Clearly, this is not a correct conclusion. The correct conclusion would be “Some burgers may or may not be pizzas”.

II. Some pizzas are sandwiches.

Since no pizza is a sandwich, therefore no sandwich can be pizza. Hence this conclusion does not follow.

Therefore, none of the conclusions are correct.

Practice Exercise 2:

Statements: 

Some pens are pencils.

No books are pens.

Conclusions:

I. No pens are books.

II. Some pencils are books.

We can draw the Venn diagram representation of the statements as shown:  

Venn Diagram Representation of Practice Exercise 2

Since we are not given any relation between books and pencils, there is a possibility that some books might be pencils as well. We have represented this possibility with a dotted circle in the Venn diagram.

Now let’s see which of the conclusions are correct:

I. No pens are books.

Since no books are pens, therefore, no pens are books is a valid conclusion.

II. Some pencils are books.

As we can see in the Venn diagram, this is only a probable conclusion. The correct conclusion would be “Some pencils being books is a possibility”.

Therefore, only I is the correct conclusion.

Practice Exercise 3:

Statements: 

All cars are buses.

Some buses are trains.

Conclusions:

I. Some trains are cars.

II. No train is a car.

We can draw the Venn diagram representation of the statements as shown:  

Venn Diagram Representation of Practice Exercise 3

Since we are not given any relation between trains and cars, there is a possibility that some trains might be cars as well. We have represented this possibility with a dotted circle in the Venn diagram.

Now let’s see which of the conclusions are correct:

I. Some trains are cars.

This is a probable conclusion. It excludes the possibility of no train being a car. The valid conclusion would be “Some trains being cars is a possibility”.

II. No train is a car.

Again, this is a probable conclusion. It excludes the possibility of some trains might be cars. So, this conclusion does not follow as well.

Since either some trains would be cars or no train would be cars, therefore, either Conclusion I or Conclusion II follows.

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