Give a set that is not closed under addition

Q: Define a smallest possible set of which both {1,3,5} and {0, 3,4 } are subsets.

A: The subsets given are {1, 3, 5} and {0, 3, 4}.

Q: List all the subsets of the set                   { –1, 0, 1 }.

A: All subsets of {-1,0,1} is:

Q: What is a set?

A: Definition of the set:

Q: define a set of which both {1,3,4} and {0,3,5} are subsets find such a set with the smallest…

A: We have to find the set with smallest possible number of elements which both {1,3,4} and {0,3,5} are…

Q: Express the set in set-builder notation {24, 32, 40, 48,....,88}

A: Consider the given set. Rewrite the elements of sets as the multiple for 8. Given set=24, 32, 40,…

Q: Define Open set ?

A:

Q: .State all the subsets that apply to /2. Include an explanation supporting why v2 belongs in each…

A: Consider the given expression, 2 the value of the given expression will be, 2=1.4142135624 it can be…

Q: Provide a direct proof that a sequentially compact set must be both closed and bounded without…

A: WE GIVE A DIRECT PROOF. First, we prove that set A is closed then A is bounded.

Q: Provide a counter example that infinity intersection of open set is open

A:

Q: that the boundary of a closed set is nowhere dense in

A: Matric space

Q: True or False: If a set contains ∅ as an element, it cannot be a partition of another set. Please…

A: We know that partition of a set, is a collection of n disjoint subsets, say P1,P2...Pn that…

Q: 26

A: The objective is to find an infinite collection of closed sets whose union is not closed.

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A:

Q: Give an оп ехат each of which example of a set with three elements is a xet.

A:

Q: Express the set using the roster method. the set of natural numbers less than or equal to 6.

A: Given: the set of natural numbers less than or equal to 6. To express: The given set in roster…

Q: Show that any finite union of Nowhere Dense Sets is Nowhere Dense.

A:

Q: Give example open set is compact

A:

Q: What is meant by the Cardinality of a finite set? Give one example.

A: The cardinality of a set is meant by the number of elements of the given set. If the set has no…

Q: Explain what is an empty set. Give relevant example along with.

A: Empty set

Q: Explain what is a finite set. Give relevant example along with.

A:

Q: A set which has ho element is said to be

A: A set with no elements = { }

Q: define sets.

A: A set is a collection of well defined objects.

Q: List all subsets of the given set. (α, β, Γ, Δ}

A:

Q: Give an example of a bounded set that has infinitely many isolated points

A:

Q: subset

A:

Q: Prove that the greatest member of a set, if exits, is the least upper bound of the set.

A:

Q: The infinite in tersection of -pon Set is ofen set.

A:

Q: two example of open set in R, closed set in R, and the closure of that set

A:

Q: What is meant by Union of sets?

A:

Q: Give an example of a countable collection of bounded sets whose union bounded, and an example where…

A: Let A1 and A2  are bounded sets

Q: prove that empty set is a subset of every set

A: We have to prove that empty set is a subset of every set = ?

Q: Give two evamples that infinite intersection of open Sets not be open. may

A: See the attachment

Q: Prove T = { ... , −56, −42, −28, −14, 0, 14, 28, 42, ... } is a countable set

A:

Q: How many elements does the successor of a set with n elements have?

A: Successor of the set, A is formed by adding an element {A} to the set. So, successor of A will be A…

Q: Define a set of which both {1, 3, 4} and {0, 3, 5} are subsets. Find such a set with the smallest…

A: {0,1,3,4,5} is the smallest set that contains {1, 3, 4} and {0, 3, 5} as sub-sets.

Q: Select the regions that correspond to the set AN BNC°.

A:

Q: The closare of a set is smallest closed set containing s صواب ihi

A: Let S be a subset of X: S⊆X. Let M be the closure of S. Then M is the smallest closed set which…

Q: determine the number of subsets of a set with 21 elements

A: To determine the number of subsets of a set with 21 elements

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A: Consider the given set A = {a, b, c}. A proper subset of a set A is a subset of A that is not equal…

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:

Q: ) Find an example of an infinite collection of closed sets whose union is not closed.

A: Any closed interval is closed in R. From that we created this example.

Q: 2. Write the set of positive odd integers in set-builder notation.

A:

Q: The intersetion of in finite open sets heed not to be open.

A:

Q: Suppose * is a binary operation on a set S. Which statement best describes problem?

A: Given that * is a binary operation on a set S.

Q: how that the union of a finite. number of bounded sets is bounded

A: A statement is given as, 'the union of a finite number of bounded sets is bounded. The objective is…

Q: Give an example of a set in R ^ 2 with the usual topology that does not have any subset (not…

A: Given that R2 with the usual topology. The aim is to find an example of the set  R2 with the usual…

Q: is The set

A:

Q: Prove that the set of all finite subsets of ω is countable. (Set theory)

A: The objective is to prove that the set of all finite subsets of ω is countable.

Q: Prove that the union of any number of open sets in Ris open.

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.