Prove that if A is an enumerable set all of whose members are also enumerable sets,...

Prove that if A is an enumerable set all of whose members are also enumerable sets, then UA is also enumerable.

Expert Solution

Here Si is an enumerable set whose members are also enumerable sets.

Colby Messinger answered 2 years ago

For each of the following sets, prove that thay are convex sets or not. Also graph...

For each of the following sets, prove that thay are convex sets or not. Also graph the sets. a) ? 1= {(?1 , ?2 ): ?1 ^2 + ?2^2 ≥ 1} b)?2 = {(?1 ,?2 ): ?1 ^2 + ?2^ 2 = 1} c)?3 = {(?1 , ?2 ): ?1 ^2 + ?2 ^2 ≥ 1}

1. Prove that if a set A is bounded, then A-bar is also bounded. 2. Prove...

1. Prove that if a set A is bounded, then A-bar is also bounded. 2. Prove that if A is a bounded set, then A-bar is compact.

Prove or Disprove The set of all finite strings is undecidable. The set of all finite...

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Prove that isomorphism is an equivalent relation on the set of all groups.

The intersection (∩) of two sets (s1, s2) is the set of all elements that are...

The intersection (∩) of two sets (s1, s2) is the set of all elements that are in s1 and are also in s2. Write a function (intersect) that takes two lists as input (you can assume they have no duplicate elements), and returns the intersection of those two sets (as a list) without using the in operator or any built-in functions, except for range() and len(). Write some code to test your function, as well. Note: Do not use the...

Let X be the set of all subsets of R whose complement is a finite set...

Let X be the set of all subsets of R whose complement is a finite set in R: X = {O ⊂ R | R − O is finite} ∪ {∅} a) Show that T is a topological structure no R. b) Prove that (R, X) is connected. c) Prove that (R, X) is compact.

Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. If...

Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. If A and B are sets then (a) |A ∪ B| = |A| + |B| − |A ∩ B| and (b) |A × B| = |A||B|. 2. If the function f : A→B is (a) injective then |A| ≤ |B|. (b) surjective then |A| ≥ |B|. 3. For each part below, there is a function f : R→R that is (a) injective and surjective. (b)...

DISCRETE MATH 1.Prove that the set of all integers that are not multiples of three is...

DISCRETE MATH 1.Prove that the set of all integers that are not multiples of three is countable.

1) a) Prove that the union of two countable sets is countable. b) Prove that the...

1) a) Prove that the union of two countable sets is countable. b) Prove that the union of a finite collection of countable sets is countable.

Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. Let...

Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. Let S = {0, 1, . . . , 23} and define f : Z→S by f(k) = r when 24|(k−r). If g : S→S is defined by (a) g(m) = f(7m) then g is injective and (b) g(m) = f(15m) then g is not injective. 2. Let f : A→B and g : B→C be injective. Then g ◦f : A→C is injective. 3....

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