**DeMorgan’s Laws of Boolean Algebra **

DeMorgan’s laws are extremely useful in simplifying expressions in which a product or sum of variables is inverted.

**The two DeMorgan’s laws are: **

(i)

This law expressed as the complement of a product is equal to sum of complements, i.e. complement of two or more variables used in AND gate is same as the OR of the complement of each individual variable.

Both the columns. and are identical, Hence Proved.

(ii) This theorem expressed as the complement of sum is equal to the product of complements, i.e. complement of two or more variables used in OR gate is same as the AND of the complements of each individual variable.

Both the columns and are identical, Hence Proved.