# De Morgan's Theorem Boolean Algebra

Published on 29-Jun-2022

## De Morgan has two theorems

1. The result of the complement of the sum of the two variables A and B is equal to the product of the complement of the equal variables.
2. The answer of the complement of the product of the two variables A and B is equal to the sum of the complements of the variables.

### First theorem:

The logical or operational complement of the variables of a Boolean expression is equal to the logical and operational value of the compliment value of those variables.
For example, if the two variables of a Boolean expression are X and Y, then (X + Y) will be ′ = X′.Y ′.  Similarly, for N number of variables (X1 + X2 + …… .. + XN) ́ = X1́.X2́ …… .. XŃ.

### Second theorem:

The complement of logical and operation of the variables of a Boolean expression is equal to the logical or operation of the compliment value of those variables.
For example, if the two variables of a Boolean expression are X and Y, then (X.Y) will be ́ = X́ +.  Similarly, for N number of variables (X1.X2. …… .. .XN) Ń = X1́ + X2́ + …… .. + XŃ.

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