Home Identity Domination Associative Commutative Distributive Review

Domination Laws: The complement is used in the operations to form these laws. The idea behind these laws is that if the first number is 1 then the negation of 1 is 0.

In equation 1, the numbers are opposite therefore in any order : 0OR1 is equal to 1.

In equation 2, using the AND operation there is no way that the solution could be 1 because both x's have to be equal to 1. There is no way this can happen because of the complement operator.

Examples:

1) x V ¬x = 1

1) x ^ ¬x = 0

Boolean Complement

Boolean Sum

Boolean Product

X  V¬x Solution
0 1 1
1 0 1
X  ^¬x Solution
0 1 0
1 0 0
CS 330