Explain the idea of cardinality. When is a set denumerable? Show that the union of two denumerable sets is denumerable.

Q: Write true otherwise false if the pairs of sets are equal,{{1}},{1,{1}}

A: Two sets A and B are equal if A and B  have the same elements.

Q: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.) {x | x is a…

A: In roster notation, all the elements of a set are listed. In this notation each element is separated…

Q: 3.5 Can two disjoint sets be close? Justify your answer using an example.

A:

Q: Give the cardinality of the set. (If the set has cardinality ℵ0, enter ALEPH NULL.) {−995, −994, .…

A: This is a problem related to sets. Cardinality of the function is generally defined by number of…

Q: Give an example to show arbitrary union of open sets is again open. Is the result true for arbitrary…

A:

Q: Which set has higher cardinality: N or Z? Explain with example

A: Cardinality: The cardinality of a set A is the number of elements present in the set A. We denote…

Q: true or false and why ? The set [0,1] has the same cardinality as ℝ .

A: True. See the attachment

Q: can two disjoint sets be close? Justify your answer using an example.

A: We know that any closed interval of the form [a,b] is an closed set. We use this fact further.

Q: If a set A has 63 proper subsets, what is |A|? *

A: Solution...

Q: Give the cardinality of the set. (If the set has cardinality No, enter ALEPH NULL.) {-31, –30, .·,…

A:

Q: true or flase? Every infinite set is unbounded.

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: Explain and give a simple example that shows that the intersection operation on sets is symmetrical.

A: Answer

Q: (aib} oPen set is [arb) ofen? ? closed set Is Is QoPen set

A:

Q: Give example open set is compact

A:

Q: Define Closed sets ?

A: Closed sets are defined as a set which consists all of their limits points. It is also defined as…

Q: 6 All open sets are bounded.

A: Some times true

Q: Use the definition of two sets have the same cardinality to prove that interval (0,2] has the same…

A:

Q: Give the cardinality of the set. (If the set has cardinality ℵ0, enter ALEPH NULL.) {−31, −30,   ,…

A: We have to find cardinality of set

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

A: Empty set

Q: Describe the set ?={?:|?^2−5|>6} as a union of finite or infinite intervals.

A: The given set is A = {x: |x2–5|>6}. Apply the absolute rule on the condition as follows.

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

A:

Q: Do infinite uncountable sets have the same cardinality? If yes explain why. If no give a counter…

A: No. Infinite uncountable sets may have different cardinality.

Q: What set is in another class of infinity that is bigger than N?

A: We know that N represents set of natural number which is countably infinite. In order to get set…

Q: What is meant by the term open interval in sets? Give example.

A: Open interval means it does not include the end values of the given set.

Q: Show that the set given in the image below is non convex. Please prove the result mathematically…

A: A set is said to be convex if for any two points in the set the line segment joining those points is…

Q: True or False a null set is an element of (-2,-1,1,4)

A: The given set is  (-2,-1,1,4)  Null set is not the element of every set. It is the subset of every…

Q: Describe the intersection and union of sets. How do they differ?

A: Definition : (1) Intersection of the sets : The intersection contains the elements that the two sets…

Q: Determine if the union/intersection of two open sets is always open then determine if the…

A:

Q: Express the set using set-builder notation. Use inequality notation to express the condition x must…

A: Set builder notation is a mathematical notation used to express the elements in a set.

Q: Proving a divisibility relation is transitive

A:

Q: Show that the following pair of sets have the same cardinality. A = (5, 9] and B = (1, 2) ∪[4, 7]

A: Two sets A and B have the same cardinality provided there is a bijection from A to B.

Q: Give the cardinality of the set. (If the set has cardinality ℵ0, enter ALEPH NULL.) {−31, −30, ...…

A: Solution: The objective is to find the cardinality of the given set

Q: Determine whether the set if finite or infinite The set of  of odd numbers greater than 3.  is is…

A: We need to determine whether the given set is finite or infinite. Let A = the set of odd numbers…

Q: i) show that a closed interval is a closed set;

A: Note: According to bartleby we have to do only first question please upload the question separately.…

Q: Please help me with this. Use element argument to prove the statement. Assume that all sets are…

A:

Q: Give the cardinality of the set. (If the set has cardinality ℵ0, enter ALEPH NULL.) {−998, −997, .…

A: Cardinality:                   The number of elements present in the given set is called the…

Q: The symbol Ø refers to the empty set. What is the cardinal number of the empty set?

A:

Q: Give the cardinality of the set. (If the set has cardinality 80, enter ALEPH NULL. {-992, –991, .…

A: Cardinality of finite set is the number of elements it contains. Now the given finite set is…

Q: Prove that empty set is subset of all sets: φ ⊆ A     Please help me figure this question out.

A:

Q: Decide whether the statement is true or false. Two set A and B are equal if have the same number of…

A:

Q: Write an example of a partially ordered set which is not totally ordered. Explain the reasons. Are…

A:

Q: Which sets are compact? The set of integers L

A: The objective is to determine whether the set of integers ℤ is compact or not.

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

A:

Q: The union of a infinite number of closed set need not be a Closed set Open Set Both open and close…

A: The union of infinite number of closed sets is

Q: Let A and B be infinite sets that are countable. Do A and B necessarily have the same cardinality as…

A: Given question is Let A and B be infinite sets that are countable. Do A and B necessarily have the…

Q: show vacuous proof of statement that "empty set is a subset of any set"

A:

Q: Give the cardinality of the set. (If the set has cardinality ℵ0, enter ALEPH NULL.) {47, 48, . . .…

A: Cardinality of a set is the number of elements in a set.

Q: The union of the universal set and any of its subset is * none of the choices cannot be determined…

A: our objective is to conclude

Q: How do we denote the empty or null set?

A: A set is said to be an empty set or a null set if there is no element in it.