B. Let S and T be sets of real numbers, and define S. T to be {x.y:x e Sandy € T}. Show that if S and T are both bounded, then S T is also bounded.

Q: Consider sets A and B with |A| = 7 and |B| = 4. How many functions f: A → B are surjective?

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Q: Which of the following sets are well-ordered. Justify youranswer carefully.A.{x:xEZ, X…

A: A set of numbers is well ordered when each of its nonempty subsets has a minimum element.

Q: this question and subsequently, let a₁, A2,..., a5 denote these numbers: 2,2,1,7,3 Let X denote the…

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Q: T T T T F F F F For sets A and B, suppose for all x E A it follows that x & B, then AnB = q. For…

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Q: Decide, among the following sets, which sets are subsets of one and another:A = { x : x ∈ R and x…

A: A = { x : x ∈ R and x satisfy x2– 8x + 12 = 0 } ={ x : x ∈ R and x satisfy (x-6)(x-2)= 0 }= {2,6} B…

Q: Assume that a and b are real numbers such that a <b. Prove that the interval (a,b) is an open set.…

A: Given that a and b are real numbers and a&lt;b. Prove that (a,b) is an open set

Q: help.

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Q: 9. Given an infinite collection An, n=1,2,... of intervals of the real line, their intersection is…

A: Let An : = [ n ,∞)  where  n = 1,2, 3 .....  . So { An } n∈ℕ is an example of infinite collection…

Q: Let a = and a = The set (a, a, ) will span R unless h = (If there are no values of h that make the…

A: For an n-dimensional vector space any set of n linearly independent vectors will span the vector…

Q: 1. A x (BNC) = (A × B)n (A x C). X

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Q: If A and B are nonempty, bounded, and satisfy A c B then sup A < sup B. If sup A < inf B for sets A…

A: a) Given that A,B are non empty sets, and A⊂B The objective is to show that supA≤sup B Since it is…

Q: Which of the following is true for all sets S and T? Select one: O A. SOT SOT B. SOT SUT C. SUT SOT…

A: see below the answer and explanation

Q: Let A and B be two measurable sets prove that if ASB then BIA is measurable and m(B\A)=m(B)-m(A)

A: The given problem is related with measure theory. Given that A and B are two measurable sets.  We…

Q: Let F = [−2, 3) ∪ {−3, π}. Determine max F, inf F,  interior of F, boundary of F,  and closure of F.

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Q: Which of the following sets is uncountable ? Select one: O a. {EN||x − 7| > |x|} O b. R\Z O c. 2Z x…

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Q: Is the set {(a₁, A2, A3, ...) € l² : |an| ≤ compact in 2? √n

A: As per the question we are given a set consisting of the infinite sequence : (a1 , a2 , a3 , ..., )…

Q: Given the following sets: U=(set of real numbers) %3D A = (x| x is a positive real number) %3D B =…

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Q: dentify the least upper bound and greatest lower bound of the following sets. If it cannot be…

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Q: If Do, D1,..., Dn... nEN, are dense open sets of reals, then the intersection D = 0 Dn is dense in…

A: Condition: Dn is the open dense sets of reals, for all n∈ℕ. To find: Intersection of infinite open…

Q: Let, X, Y, Z be sets of sizes x, y and z respectively. Let W = Xx Y and E be the set of all subsets…

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Q: Let X and Y be sets with A,B ⊆ X. If f : X →Y is a function, prove that f(A∪B) =f(A)∪f(B)

A: I am going to solve the problem by using some simple algebra to get the required result of the given…

Q: Choose and work 2 problems only. 1. Let E be a bounded infinite set and let x = inf E. Prove : if x…

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Q: Let X be a set. Show that P(X)÷ X.

A: Solution:Let X ba a set.To Prove: P(X)≠X

Q: Suppose F and G are families of sets. Prove that (UF)n (UG) ≤ U(F N G) iff VA EFVBE G(An BCU (FNG)).

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

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

Q: Let R = {x € Z | x is divisible by 2}. Determine which of the following sets are subsets of R.…

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Q: Let a, b ER and a < b. Prove that the intervals (0, 1) and (a, b) are equivalent. Moreover, if c, d…

A: It is given that a,b∈ℝ and a&lt;b. The objective is to prove the intervals 0,1 and a,b are…

Q: Consider sets A and B with |A| = 12 and |B|| 8. How many functions f : A → B are surjective?

A: We will find out the required value.

Q: A set L cR is convex if:

A: In this question, we have to find the correct option for the convex set L⊂Rn  here we use the direct…

Q: Which of the following sets are equal? A = {b, g, j} B= {x, y} C= j, g, b} D= {x|1sx<3 and xEN} J=…

A: Here, A = {b, g, j} B = {x, y} C = {b, g, j} D = {1, 2, 3} J = {0, 2, 4, 6, .....} K = {6, 8, 10,…

Q: B. Let S and T be sets of real numbers, and define S. T to be {x.y:x e Sandy € T}. Show that if S…

A:

Q: Let Si = { x ∈ R ∣ x > i } , i=0,1,2,... Are the sets S1, S2, S3 . . .  are mutually disjoint?

A: If two sets A and B are mutually disjoint, then A∩B=ϕ . Define the sets S1 , S2 , S3 as follows.…

Q: 5. Let the universal set be R, the set of all real numbers, and let A = {x € R| – 4 <x< 1},B = {x €…

A: Given the universal set as ℝ, the set of all real numbers. Let A={x∈ℝ| -4≤x&lt;1}, B={x∈ℝ|…

Q: Let A and B be non-empty subsets of R. and let C = {2 +y: * € A,y € B}. Show that inf A+ inf B = inf…

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Q: 2}

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