22. Let 2 be a non-empty set and let C be all one point subsets. Show that o (C) = {A C 2 : A is countable }{AC: A° is countable }. %3D

Q: Define the partially ordered set (N",<) as follows: x < y if Xi < Yi for all 1<i<n. For example, (2,…

A:

Q: 4. Prove that, for any sets A and B, it is true that A C B iff AnB = A. Hint. There are two…

A: The intersection is a set operation. The intersection of finite number sets consists of elements…

Q: 2. Let A = {r|x is older than 25}, B = {y|y_is older than 50}, C = {z |z is between 20 and 30}. Draw…

A: The question is related to sets. The solution is explained below.

Q: Consider all subsets of size four of the set (1,2,3...20) how many of these have a nonempty…

A: Solution :-

Q: 8. Give an example of each of the following : (a) a set which is a nbd. of each of its (b) a set…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 7. Show that if S x T is a closed subset of R?, then S and T are closed subsets of R.

A:

Q: 1. A is a well defined collection of 2. objects called 3. If A and B are sets, then B C A iff In tho…

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: 2. Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not exactly?

A: No, there is no set A that satisfies A={A}. Let A is an empty set, i.e.  A=  or  A=ϕ, in which…

Q: 4. Let S be any nonempty set with the operation a * b = a. Is (S,*) a semigroup? Is it commutative?

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Consider the set T = {..., −34, −17, 0, 17, 34, ... } with the usual definition of less than (a0).…

A: Completeness property of real numbers:  Every non-empty set of real numbers that has an upper bound…

Q: Determine whether the set S = {1, x², 3 + x²} spans P2. O S spans P2. O s does not span P2.

A: Consider the given set S. S=1,x2,3+x2 Now, make the matrix from the given set. 103000011

Q: Suppose is dhe iavene faction of a diffarentiable šunc- tica fand let Glu) -1/r . E3) - 2 and /3) -…

A: G(x)=1f-1(x)f(3)=2 , f'(3)=1/9

Q: Q.A. Is the nonnepatibe orthaut %(D t. a cohvek set?

A:

Q: 9) Find the power set of each of these sets, where X, y are distinct elements: (a) {x, y} (b) {x, y,…

A:

Q: 21. For E = {a, b}, construct dfa's that accept the sets consisting of (a) all strings of even…

A: NOTE: According to bartleby  guidelines we have to answer only first three subparts please upload…

Q: Q.A. Is the nonnepatbe orthaut t. a cohvek set?

A: Answer is negative

Q: Let X, Y subset U. Suppose that n(X)= 22, n(Y)= 20, and n(X intersect Y)= 16. How many elements are…

A: Let X,Y be subsets of U.  nX=22 , nY=20 and nX∩Y=16 It is given that nU=40. Find nX'∪Y:

Q: 4.2. Let S be the open set consisting of all points z such that |2| < 1 or |z – 2| < 1. Show that S…

A: Connected set: If any two points of a given set can be joined by a continuous polygon arc such that…

Q: The number of non-empty subsets of B is |{S:SC A, S = 3 and Sn B = 0}| = max {|S|: SC AUB, SNA| is…

A: Given that A and B are finite sets satisfying A=6, B=7, A∩B=2. Since, B=7. So, total number of…

Q: 2, Say whether the Runction is even, odd, or neither. Give reasanS for your dnswer. ga) = x"+ x*-1

A:

Q: prove that i } X is a Coun table set and P: X>Y is asurjecbive then Y is Countable

A: Note: X denotes cardinality of X, that is number of elements in the set X. If X is countable means…

Q: Let R = Zg, and let N = R³. Determine whether or not X = {(4, 5, 4), (4, 5, 2), (2, 2, 3)} is a free…

A: It is given that,  R = ℤ8  and  N = R3. We have to determine that whether the set,  X = 4, 5, 4, 4,…

Q: (10) Show that the set A = {a € Q : a² < 2 or a < 0} is a %3D cut.

A:

Q: (d).Show that the derived set E′E′ of any set EE is closed.

A: To show that derived set E′ of any set E is closed.

Q: 3. Let M and N be nonempty set such that M = N, then |M| = |N|. %3D

A:

Q: Show that the sete S = {x E R]x = m/3, where m E N with m > 4} is countable

A:

Q: shows that there is no topology in X based on the family B = {{a, b}. {a, b, d}, {b, d, c}}

A:

Q: List the elements of set D = { x:x є N, x is a multiple of 5} where N= {1, 2, 3, ...}.

A:

Q: (3) Let S = {; Find with prove :m eN,n E N}. %3D suprenum of S. (4) What is an unbounded set?

A:

Q: Let C be a nonempty subset of a bounded set D. Why does inf C and sup C exist? Show that (c) inf D ≤…

A:

Q: If A is a countable set and B is an uncountable set, then the MOST we could ever say about A U Bis…

A: We have given the three MCQ questions about countability and uncountability . We have to choose the…

Q: 1. Decide whether the folloring stabe ments ae false . Justify true or (a) YxeTR, ¥yeR, x²-y² z xy…

A: 1. a ∀ x ∈  R, ∀ x ∈  R, x2+y2 ≥ 2xy  TRUE. Because,  ∀ x ∈  R, and ∀ x ∈  R we have (x-y)2 ≥ 0.…

Q: Consider the set A = {xy : x ∈ N, y ∈ N} = {1, 2, 22, 23, 24, ...., 3, 32, 33, 34,......, 4, 42, 43,…

A:

Q: Let'Y be the set of f bleod types B+ Hat type Connot donate blood to.

A: Here, X is the set of blood types AB- can donate blood. AB- can donate blood to AB- and AB+ Hence,…

Q: Show that B,(x) is open set with respect to 7 for all r> 0.

A:

Q: 7. Show that the Obenchain class LOb(B) is a convex set.

A: Given: To show the Obenchain class LOb (β) is a convex set is given as,

Q: 6. Give an example of a set S which is (i) bounded above but not bounded below, (ii) bounded below…

A: (i). Let  S = { ..., -5, - 4, - 3, - 2, - 1 }

Q: let A Set bounded belou, erove that C. inf A Inf C A ン

A:

Q: 4. Prove that the set Z is a closed set in R.

A:

Q: 1. Prove or Disprove: For all sets A and B, MUB- M+ B

A:

Q: (4.1) For sets A and B. prove that P(AB) = P(A)~P(B).

A:

Q: Suppose that a,beG such that a = m and b =n with Gcd (m,n) = 1. Then n | is in mn

A: Suppose that a, b∈G such that a=mb=n and Gcdm, n=1 i.e., m and n are relatively prime. We will find…

Q: Let S be a set of n elements. Find the number of distinct subsets of S.

A: Given: Let S be a set of n elements.

Q: Show that the set EE is: (ii). Closed iff E¯=E

A: Show that the set E is Closed iff E¯=E

Q: 3. Consider three finite sets A, B and C. Show that: (a) (b) (c) (AB) x C = (A ×C) \ (B × C ); (AUB)…

A:

Q: Determine whether the set S = {1, x², 9 + x²} spans P2. %3D O S spans P2. O s does not

A: Introduction: Vectors' span, It is the collection of all linear combinations of a number of vectors.…

Q: 2- Moke the definitions of open and closed sets. x =Larbic,d,eļ and ノ closed subsets of (x,T) space,…

A:

Q: 2.3 Show that the following sets don't satisfy the law of contradiction and the law of excluded…

A: part(a) GIVEN μAx=11+x TO SHOW: given function don't satisfy the following laws 1) law of…