Show that the class of all finite unions of closed-open intervals on the real line is a ring of sets but is not a Boolean algebra of sets.

Related BrainMass Solutions

• Show that the class of all finite unions of closed-open intervals on the real line is a ring of sets but is not a Boolean algebra of sets.

  124060 Show that the class of all finite unions of closed-open intervals on the real line is a ring of sets but is not a Boolean algebra of sets.

• Show that the class of all finite subsets ( including the empty set) of an infinite set is a ring of sets but is not a Boolean algebra of sets.

  123550 Show that the class of all finite subsets ( including the empty set) of an infinite set is a ring of sets but is not a Boolean algebra of sets.

• Boolean Ring Question

  469039 Boolean Ring Question Let R be a Boolean ring and let X be the set all maximal ideals of R. Put a topology on X by taking sets of the form Dr = {M ∈ X | r ∈/ M}, r is in R, as a basis for the open topology.

• Class of all finite unions of sets of the form A×B

  Show that the class of all finite unions of sets of the form A×B with A belongs to the family set A and B belongs to the family set B is a ring of subsets of X×Y.

• Prove that a given collection of sets is a sigma-algebra

  341863 Prove that a given collection of sets is a sigma-algebra Let A be a sigma algebra of subsets of R (Real numbers) and suppose I is a closed interval which is in A.

• Working with Topological Spaces

  We know K is a closed set since X-K is open. A={0} is also a closed set. We note 0 is a limit point of K, but 0 is not in K. For any open neighbors U(A) of A, U(A) will contain many points in K and thus breaks the T4 rules.

• Free Boolean Algebra

  This implies that, for any set D, the image F(B) of the free Boolean algebra B on D is isomorphic to the free Boolean ring on the set D.

• Finiteness of Sets

  Hence is an open set. Problem (d) For finite collection of closed sets , we want to show that is closed. Because each is closed, then the complementary set is open. From the result in (c), is an open set. So is closed. Done.

• subset

  Determine (up to isomorphism) all semisimple rings of order 1008. How many of them are commutative? (Recall that finite division rings are fields.) 2. A ring R is Boolean if x2 = x for all x  R.