Fraternities in {{org-stub}}
- Alpha Chi Omega
- Alpha Delta Pi
- Alpha Kappa Delta Phi
- Alpha Omicron Pi
- Alpha Rho Chi
- Alpha Sigma Alpha
- Alpha Sigma Phi Philippines
- Alpha Tau Omega
- Alpha Xi Delta
- Beta Chi Theta
- Gamma Tau
- Delta Chi
- Delta Phi Epsilon
- Delta Upsilon
- Zeta Phi Beta
- Zeta Tau Alpha
- Iota Nu Delta
- Iota phi theta
- Kappa Psi
- Sigma Iota Rho
- Sigma Pi Phi
- Sigma Psi
- Phi Alpha Kappa
- Phi Beta
- Phi Mu
- Phi Sigma Kappa
- Phi Sigma Rho
- Phi Sigma Sigma
The many faces of C. C. Moore
- Charles Chilton Moore - editor of one of the nation's first journals promoting atheism, Blue Grass Blade.
- CC Moore - Porn star
- CC Moore & Co Ltd, Dorset - Discount bait suppliers
- C.C. Moore Co., Fullerton, CA - "Manufactures EMI/EMC facilities to meet FCC and CE test requirements." - Founded by, get this: Charles Chilton Moore, Sr.! There's another one!!!
- C. C. Moore - "was instrumental in bringing the Negro fair to Huntsville"
Boolean algebra
In mathematics, specifically in abstract algebra, a Boolean algebra is an algebraic structure that generalizes structures arising both in set theory and in logic. The set theoretic operations of intersection, union, and complementation, and the set theoretic relation of subset inclusion follow the same algebraic rules as the logical operations of AND, OR, and NOT, and the logical relation of logical implication. A Boolean algebra is a structure on which these rules can be studied in a general context, without referring specifically to set theory or to logic. Boolean algebras are named after George Boole.
Formally, a Boolean algebra is a partially ordered set, equipped with two binary operations, and with one unary operation. The operations must follow a list of axioms, given below. In order to understand this definition, we consider the two examples already mentioned:
- For our set, we take the collection of subsets of a three-element set: {{}, {x}, {y}, {z}, {x,y}, {x,z}, {y,z}, {x,y,z}}. We order this set according to the relation of subset inclusion ([insert symbol]) (as illustrated), and define on it the binary operations of union and intersection, and the unary operation of complementation, in the usual way. This set of subsets, its ordering, and its operations, compose a Boolean algebra.
- Now for our set, we choose a two element set, with binary truth values for elements: {TRUE, FALSE}. Our ordering relation is logical implication ([insert symbol]), the two binary operations are AND and OR, and the unary operation is NOT. The usual rules, such as NOT TRUE = FALSE apply to these operations, and we thus have a very small two-element Boolean algebra, which is exploited in the Boolean logic studied in computer science. This simple Boolean algebra generalizes to larger ones in which truth values may take on a spectrum of values between FALSE and TRUE.
Boolean algebras are sometimes called Boolean lattices, because every Boolean algebra also meets the definition of a lattice: a partially ordered set with two binary operations obeying certain axioms. The axioms for a Boolean algebra imply the axioms for a lattice, so every Boolean algebra is a lattice. Suggestively, the symbols used for logical AND and OR, "∧", and "∨", are the same symbols used for the lattice operations of "least upper bound" (or "join" or "supremum") and "greatest lower bound" (or "meet" or "infimum").
The lattice interpretation helps in generalizing to Heyting algebras, which are Boolean algebras freed from the restriction that either a statement or its negation must be true. Heyting algebras correspond to intuitionist (constructivist) logic just as Boolean algebras correspond to classical logic.