Mathematics

# De Morgan’s Law

De Morgan, a 19th-century British mathematician his rules in proportional logic and Boolean algebra are expressed as,

the negation of a conjunction is the dis junction of the negations; and
the negation of a dis-junction is the conjunction of the negations;

or

the complement of the union of two sets is the same as the intersection of their complements; and
the complement of the intersection of two sets is the same as the union of their complements.

DeMorgan’s Theorem Statement:

1. The complement of the sum of two or more variables is equal to the product of the complements of the variables. If X and Y are the two logical variables, then according to the De Morgan’s Theorem we can write: (X + Y)’ = X’.Y’.

2. The complement of the product of two or more logical variables is equal to the sum of the complements of the variables. If Z and Y are the two logical variables, the according to the second law of De Morgan’s theorem we can write: (X.Y)’ = X’ + Y’