Algebra 2.5: Apply the Distributive Property, Pages 96
... Name_______________________________________________________ Period_______ ...
... Name_______________________________________________________ Period_______ ...
Word Pro - set1 - Kennesaw State University | College of Science
... The set that contains no elements is called the empty set or null set and is denoted by π or by {}. A universal set is the set that contains all the elements for any specific discussion. It is denoted by U. An ordinal number describes the relative position that an element occupies. ...
... The set that contains no elements is called the empty set or null set and is denoted by π or by {}. A universal set is the set that contains all the elements for any specific discussion. It is denoted by U. An ordinal number describes the relative position that an element occupies. ...
Chapter 2: A little Set Theory Set Theory By a set we shall mean a
... considered to lie. We are thereby restricting the ability to construct something like: “The set of all sets.” By the complement of a set A we mean all elements in our Universal set which do not lie in A. Thus in the integers the complement of A = {2, 5, 6} would be B=1, 3, 4, 7, 8, 9, ... where by t ...
... considered to lie. We are thereby restricting the ability to construct something like: “The set of all sets.” By the complement of a set A we mean all elements in our Universal set which do not lie in A. Thus in the integers the complement of A = {2, 5, 6} would be B=1, 3, 4, 7, 8, 9, ... where by t ...
3-8 Unions and Intersection of Sets
... In your left pocket, you have a quarter, a paper clip, and a key. In your right pocket, you have a penny, a quarter, a pencil, and a marble. What is a set that represents the different items in your pockets ...
... In your left pocket, you have a quarter, a paper clip, and a key. In your right pocket, you have a penny, a quarter, a pencil, and a marble. What is a set that represents the different items in your pockets ...
Activity: The Distributive Law and Factoring
... This should agree with your intuition that a1 = a, ...
... This should agree with your intuition that a1 = a, ...
Mathematics 310 Robert Gross Homework 7 Answers 1. Suppose
... (a) Show that R ⊕ S is a ring. (b) Show that {(r, 0) : r ∈ R} and {(0, s) : s ∈ S} are ideals of R ⊕ S. (c) Show that Z/2Z ⊕ Z/3Z is ring isomorphic to Z/6Z. (d) Show that Z/2Z ⊕ Z/2Z is not ring isomorphic to Z/4Z. Answer: (a) First, the identity element for addition is (0R , 0S ), and the identity ...
... (a) Show that R ⊕ S is a ring. (b) Show that {(r, 0) : r ∈ R} and {(0, s) : s ∈ S} are ideals of R ⊕ S. (c) Show that Z/2Z ⊕ Z/3Z is ring isomorphic to Z/6Z. (d) Show that Z/2Z ⊕ Z/2Z is not ring isomorphic to Z/4Z. Answer: (a) First, the identity element for addition is (0R , 0S ), and the identity ...
Sections 2.1/2.2: Sets
... • Subset of a set: Set A is said the be a subset of B, denoted A ⊆ B, if and only if every element of A is also an element of B. • Proper subset: A is a proper subset of B, denoted A ⊂ B, if A ⊆ B and B has an element that is not in A. • Disjoint sets: A and B are disjoint if they have no elements i ...
... • Subset of a set: Set A is said the be a subset of B, denoted A ⊆ B, if and only if every element of A is also an element of B. • Proper subset: A is a proper subset of B, denoted A ⊂ B, if A ⊆ B and B has an element that is not in A. • Disjoint sets: A and B are disjoint if they have no elements i ...
Birkhoff's representation theorem
This is about lattice theory. For other similarly named results, see Birkhoff's theorem (disambiguation).In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations correspond to unions and intersections of sets. The theorem can be interpreted as providing a one-to-one correspondence between distributive lattices and partial orders, between quasi-ordinal knowledge spaces and preorders, or between finite topological spaces and preorders. It is named after Garrett Birkhoff, who published a proof of it in 1937.The name “Birkhoff's representation theorem” has also been applied to two other results of Birkhoff, one from 1935 on the representation of Boolean algebras as families of sets closed under union, intersection, and complement (so-called fields of sets, closely related to the rings of sets used by Birkhoff to represent distributive lattices), and Birkhoff's HSP theorem representing algebras as products of irreducible algebras. Birkhoff's representation theorem has also been called the fundamental theorem for finite distributive lattices.