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
X | V¬x | Solution |
0 | 1 | 1 |
1 | 0 | 1 |
X | ^¬x | Solution |
0 | 1 | 0 |
1 | 0 | 0 |