For N variables, DeMorgan’s theorems are expressed in the following formulas:

(1-2)

That is, the complement of the product is equivalent to the sum of the complements

(1-3)

Similarly, the complement of the sum is equivalent to the product of the complements

Applications of DeMorgan’s theorems range from deriving the composite of functions to providing alternative design to logic circuits. The objective of using these theorems in circuit design is to minimise the number of ICs required in a logic circuit.

Examples of DeMorgan’s theorem:

Applying Demorgan’s theorem to the expression we get:

 

Applying Demorgan’s theorem to the expression we get: