Laws
A law of Boolean algebra is an equation such as x∨(y∨z) = (x∨y)∨z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡, but such extensions are unnecessary for the purposes to which the laws are put. Such purposes include the definition of a Boolean algebra as any model of the Boolean laws, and as a means for deriving new laws from old as in the derivation of x∨(y∧z) = x∨(z∧y) from y∧z = z∧y as treated in the section on axiomatization.
Read more about this topic: Boolean Algebra
Famous quotes containing the word laws:
“The tide which, after our former relaxed government, took a violent course towards the opposite extreme, and seemed ready to hang every thing round with the tassils and baubles of monarchy, is now getting back as we hope to a just mean, a government of laws addressed to the reason of the people, and not to their weaknesses.”
—Thomas Jefferson (1743–1826)
“Between married persons, the cement of friendship is by the laws supposed so strong as to abolish all division of possessions: and has often, in reality, the force ascribed to it.
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—David Hume (1711–1776)
“Nothing comes to pass in nature, which can be set down to a flaw therein; for nature is always the same and everywhere one and the same in her efficiency and power of action; that is, nature’s laws and ordinances whereby all things come to pass and change from one form to another, are everywhere and always; so that there should be one and the same method of understanding the nature of all things whatsoever, namely, through nature’s universal laws and rules.”
—Baruch (Benedict)