DeMorgan’s Theorems

1. (A . B)' = A' + B'
2. (A + B)' = A' . B'

One of the most powerful identifies used in Boolean logic is DeMorgan’s theorem. Augustus and Demorgan have paved way to boolean logic by discovering the two important theorems.

DeMorgan’s First Theorem

DeMorgan’s First theorem proves that when two (or more) input variables are OR’ed and negated, they are equivalent to the AND of the complements of the individual variables. Thus the equivalent of the NOR function is a negative-AND function proving that A+B = A.B, and again we can show operation this using the following truth table.

Verifying DeMorgan’s First Theorem using Truth Table

DeMorgan’s Second Theorem

DeMorgan’s Second theorem proves that when two (or more) input variables are AND’ed and negated, they are equivalent to the OR of the complements of the individual variables. Thus the equivalent of the NAND function will be a negative-OR function, proving that A.B = A+B. We can show this operation using the following table.

Verifying DeMorgan’s Second Theorem using Truth Table