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Venn Diagram form of the Boolean Expression

Venn diagram form of Boolean Expression:

We can represent Boolean function or expression by Venn diagram and we can use Venn diagram for minimization.

Where 1 means the existence of variable A other section value of A is zero.

Example 1:

So, as per the Venn diagram Boolean expression is:

Note: Here U means universal set where U = 1

Question 1: 

What is the Boolean expression for the shaded area?

Solution:

As per the shaded area, the Boolean expression is: 

Or we can directly write

Another way:

Or we can think of another way to take the complement of the unshaded area then we get the expression of the shaded area.

So, we can take the complement. 

The Boolean expression of the shaded area is:

Example 2:

What is the Boolean expression for the shaded area?

Solution:

As per the shaded area, the Boolean expression is: 

So, option (c) is the correct answer.

We can minimize it:

Question 2:

What is the Boolean expression for the shaded area?   

Solution:

As per the shaded area, the Boolean expression is: 

So, option (a) is the correct answer.

Question 3:

What is the Boolean expression for the shaded area?   

Solution: 

As per the shaded area, the Boolean expression is: 

So, option (b) is the correct answer.