Date of Award:
5-1963
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Committee Chair(s)
Charles H. Cunkle
Committee
Charles H. Cunkle
Abstract
The purpose of this section is to define a boolean algebra and to determine some of the important properties of it.
A boolean algebra is a set B with two binary operations, join and meet, denoted by + and juxtaposition respectively, and a unary operation, complementation, denoted by ', which satisfy the following axioms:
(1) for all a,b ∑ B (that is, for all a,b elements of B) a + b = b + a and a b = b a, (the commutative laws),
(2) for all a,b,c ∑ B, a + b c =(a + b) (a + b) and a (b + c) = a b + a c, (the distributive laws),
(3) there exists 0 ∑ B such that for each a ∑ B, a + 0 = a, and there exists 1 ∑ B such that for each a ∑ B, a 1 = a,
(4) for each a ∑ B, a + a' = 1 and a a' = 0.
If a + e = a for all a in B then 0 = 0 + e = e + 0 = e, so that there is exactly one element in B which satisfies the first half of axiom 3, namely 0. Similarly there is exactly one element in B which satisfies the second half of axiom 3, namely 1.
The 0 and 1 as defined above will be called the distinguished elements.
Checksum
0f0c69fd4932af6c9c23c8eeab705601
Recommended Citation
Eggert, Jr., Norman H., "An Investigation of the Range of a Boolean Function" (1963). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 6772.
https://digitalcommons.usu.edu/etd/6772
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