# DE MORGAN'S LAWS

De Morgan’s laws relate the three basic set operations Union, Intersection and Complement.

De Morgan's First Law :

The complement of the union of two sets  is equal to the intersection of their complements.

That is

(AuB)' = A'nB'

De Morgan's Second Law :

The complement of the intersection of two sets is equal to the union of their complements.

That is,

(AnB)' = A'uB'

## De Morgan's First Law - Proof by Venn diagram

(AuB)' = A'nB'

Let's draw Venn diagram for (AuB)'.

To draw Venn diagram for (AuB)', first draw Venn diagram for (AuB).

To draw Venn diagram for (AuB)', shade the region other than (AuB).

Now, let's draw Venn diagram for (A'n B').

Draw Venn diagram for A' and B'.

Then, to draw Venn diagram for (A'nB'), find the common region of A' and B'.

The resulting Venn diagrams of (AuB)' and (A'nB') are same.

So,

(AuB)' = A'nB'

## De Morgan's First Law - Proof by Venn diagram

(AnB)' = A'uB'

Let's draw Venn diagram for (AnB).

To draw Venn diagram for (AnB)', first draw Venn diagram for (AnB)

To draw Venn diagram for (AnB)', shade the region other than (AnB).

Now, let's draw Venn diagram for (A'u B').

Draw Venn diagram for A' and B'.

Then, to draw Venn diagram for (A'uB'), join A' and B'.

The resulting Venn diagrams of (AnB)' and (A'uB') are same.

So,

(AnB)' = A'uB'

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

## Recent Articles

1. ### SAT Math Resources (Videos, Concepts, Worksheets and More)

Jul 11, 24 05:20 PM

SAT Math Resources (Videos, Concepts, Worksheets and More)

2. ### SAT Math Videos (Part - 21)

Jul 11, 24 05:14 PM

SAT Math Videos (Part - 21)