Let A, B be any sets with ACB. Then * O None of these O IP(A×B)|<|P(B×B)| O IP(A×B)|=|P(B×B)| O IP(B×B)|<|P(A×B)|

Q: Let T be a set such that if the integer x is in T, then 2(x+1) is also in T. Let integer 2 is in T,…

A: To find the correct answer.

Q: 28. Let R be a collection of sets defined by R = {x | x ¢ x}. %3D (a) Show R is not the empty set.…

A:

Q: Set A is bounded above if and only if set -A is bounded below.

A:

Q: Let A be a set. Prove that S = 0. SEP(A)

A:

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: O a. sup (A U B) exists if…

A:

Q: 3. Let {B;}je1 and {C;};e1 each be a family of mutually disjoint sets. If B; = C; for each i e I,…

A: Answer :

Q: 1. Let A be an uncountable set and B C A such that there exists a surjective function f : Z+ → B.…

A:

Q: 1. Define the following sets in extension: (i) {x:N|x< 4• 3 * x} (ii) {x,y:N|x < 6^ y< x•x-y} (iii)…

A:

Q: Let A be a bounded non-empty set. Then inf A < sup A. True False

A:

Q: Let A {a1, a2, ...} and B = {b1,b2, ...} be countably infinite sets. %3D Prove that A × B is a…

A:

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: Choose the correct option: a.…

A: Sup(A) denote  least upper bound of set A

Q: Let (Un) be a sequence of open sets in R then a) U₁is open, b) nis open.

A:

Q: Let S be an ordered set.  Let B ⊂ S be bounded (above and below). Let A ⊂ B be a nonempty subset.…

A: We can prove this by the definition of upper and lower bound

Q: Let A be a non-empty, bounded set of positive real numbers. Let B be the set consisting of numbers…

A:

Q: Let A, B be non-empty bounded sets, and A Ç B (A is a proper subset of B). Then sup A < sup B. True…

A: Let A=(1,2] and B=[1,2]

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: a. sup (A U B) exists if sup(B)…

A:

Q: Let A, B be any sets with ACB. Then O None of these O IP(BxB)|s|P(A×B)| O IP(A×B)=|P(B×B) O…

A:

Q: Let A and Bbe subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A N…

A:

Q: Let T be a set such that if the integer x is in T, then 2(x+1) is also in T. Let integer 2 is in T,…

A: Given T is set of integers with 2 belongs to T.

Q: Let A and B be nonempty sets of real numbers. If sup B exists then sup (A U B) exists if A is…

A: let A and B be nonempty subsets of reals.

Q: Let Ø denote the empty set .Prove each of the following. (a) (A-B)NCACUB)=0 For all sets A and B.

A: Union and Intersection of Sets: The union of two sets A and B is the set of all elements which…

Q: Let T and M be a non-empty families of sets with T  ⊆ M. Show that ∩T  ⊆ ∪ M.

A: Given: T and M are families of sets with T⊆M. To show: ∩T ⊆∪M

Q: The Cantor set is closed .A O dense .B O open .C O neither open nor closed.D O

A: Closed

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: O a. sup (A U B) exists if…

A: a)If sup A and sup B exists then          supA∪B=max{sup A,sup B} So supA∪B exists. First option is…

Q: Determine whether the following theorem is true or false: For all sets A, B and C, if A is a subset…

A: If X is a strict subset of Y, but X is not equal to Y which means there exists at least one element…

Q: Let T be a set such that if the integer x is in T, then 2(x+1) is also in T. Let integer 2 is in T,…

A: Given 2 is in T so 1st and 4th are possible answers.

Q: Let A and B be finite sets such that B = {b1, b2}. Prove that |A – B| < |A|.

A: We are given that A and B are two finite sets, where B= {b1, b2}.We have, |B| = 2, and let |A| =…

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: а. sup (A U B) exists if sup(B)…

A:

Q: Let A be a nonempty subset of R that is bounded below. Define the set B = {b: b is a lower bound of…

A:

Q: Prove that A is an infinite set if and only if ∀n ∈ ω, A has a subset B such that B ≈ n.

A: given that A is an infinite set let B be any set let prove this contradiction suppose assume that B…

Q: Let A and Bbe subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A N…

A:

Q: Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B…

A:

Q: x = sup(A) and if a ɛ A, with x#a , then which of the following statements is Let true? O There is…

A: Given that x is sup(A) . We have to check which of the following statement is true or false.

Q: Let X = R (or any uncountable set). Define µ* : P(X) → R by { if A is countable µ*(A) = 1 if A is…

A:

Q: 4. Let A and B be any two non-empty sets. Prove that P(ANB) = P(A)NP(B).

A:

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

A:

Q: (3.2) Indicate which of the following sets are compact in X. (a) C = {4,n € N}, X = R (b) C = Qn (0,…

A:

Q: Prove that if A is a set then so is {A} but do NOT use an argument that involves stages explicitly.

A: 3 Given A is any set. We have to prove that A is also a set. Since, A is any set Then as every set…

Q: Let A be nonempty bounded subset of real numbers, with u=sup{A}>0. Let A= for all a = 0}, then inf(-…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Let Ω be a set and A = {A ⊂ Ω : A is finite or Ac is finite }

A: given that Ω is a set and also given A ⊂Ω if Ω contains n elements  then A contains (n-1) elements…

Q: 5. If X any Y are sets, then X-Y {r€X: z4Y} If X is open set and Y is closed set. Prove that (a) X-Y…

A: Let X is open set and Y is closed set

Q: Determine if the two sets are dense in R, nowhere dense in R or somewhere in between: A=Q⋂[0,5]…

A:

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: O a. sup (AU B) exists if sup(B)…

A: If s is an upper bound for A∪B iff it is an upper bound for A and for B, so s≥supA and s≥supB   The…

Q: Let $X$ be a set and assume that p E X. Let Tp be the collection 0, X, and all subsets of X that…

A:

Q: Let A be a nonempty subset of R that is both bounded above and below and let B be a nonempty subset…

A:

Q: Let A be a nonempty subset of positive integers and B = {n + v5_ : nE A}. Show that B has a least…

A: We will use the well ordering principle to prove that B has a least element.

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: 6. Let S be a set with a finite number of elements, and let f: S→→ S be a map (a) If fis onto, can f…

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: Let F and G be a non-empty families of sets with SG. Show that ng s UG.

A: Given: F and G are two non-empty family of sets with F⊆G, To show: ∩F⊆∪G