a) State the intersecton of an indexed family of sets.

Q: 6. Show that the span of this set is all of R?. {}}

A: Let S=v1,v2,...,vn be a set of vectors in a vector space V(F) . The vector space V is spanned by S,…

Q: Define Open set ?

A:

Q: When is a set compact?

A:

Q: The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6,…

A: It is given that the universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.If A = {1, 2, 3, 4, 5} and…

Q: True or false? A∩(B∪C)=(A∩B)∪(A∩C) You should determine this by building the Venn Diagram for each…

A: Given statement is A∩(B∪C)=(A∩B)∪(A∩C)

Q: Let X={a,b,c} and Y=∅. What is X∩Y? If the set is empty type ∅, otherwise write your answer in…

A:

Q: The family of all finite subsets of a countable sets is countable.

A: Countability

Q: Q.Prove If ANB is pathwise connected set, then A andB are or disprove the following: pathwise…

A:

Q: Show that the set is infinite by placing it in a one-to-one correspondence with a proper subset of…

A:

Q: c) Create a set comprehension for the set F = {1,2,4,8 %3D

A: Solution of the problem as follows

Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

A:

Q: Let the universe of elements include these letters: p, q, r, s, t, u, v, w, x, y. The first set A…

A: The universe set contains the elements: p, q, r, s, t, u, v, w, x, y The set A contains the…

Q: Could the explanation of how each cardinality set is determined be described?

A: Cardinality :  It is the number of elements in a mathematical set. In question there are three…

Q: A and B be two sets, and A - B = . a) What can you say about sets A and B? b) Draw a Venn diagram.

A:

Q: 2 of 4 02 (Core): I can represent a set in roster notation and set-builder notation; determine if an…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Prove that the cartesian product of a countable set is countable

A: This is question related to set theory's topic countability.

Q: Let A and B be infinite sets that are uncountable. Do an and B have the same car finality as each…

A: Let A and B be infinite sets that are uncountable. Do A and B have the same cardinality as each…

Q: Let U = { a, b, c, d, e, f, g, h} be the universal set. Let A = {e, g, d, a, f}, B = {b, g, c, f}…

A: (A∩B)={a,b,c,d,e,h}B−A={b,c}(B−C)∪A={b,c,e,g,d,a,f}Explanation:

Q: 3. Give an example of sets A and B and a universal set U such that A c B. Find A and B.

A:

Q: Give an example of a countable collection of finite sets whose union is not finite.

A:

Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

A:

Q: Construct a family of sets that demonstrates R is not compact

A:

Q: 5. Show that a finite set is a closed set.

A: