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 and B, then there exists a c e R satisfying a < c< b for all a E A and b e B. If there exists a c E R satisfying a

Q: 2. Decide whether each of the following sets are finite, denumerable or uncountable. Explain each of…

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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 a, b ∈ R. Show if a ≤ b1 for every b1 > b, then a ≤ b.

A: Density Property of ℝ If x,y are real numbers with x&lt;y, then ∃ a rational number r such that…

Q: Suppose A and B are finite sets with |A| = a, |B| = b and |An B| = c. Find (a) |AB| (b) AX (AUB)|…

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Q: A={ y ∣ y ∈ N and 305< y ≤ 335} A has      subsets.  A has              proper subsets.

A: We have, A={ y ∣ y ∈ N and 305&lt; y ≤ 335} Let A and B be two sets. We say that A is a subset of B…

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: Let a, b € R. Show that if a ≤ b₁ for every b₁ > b, then a ≤ b. (Hint: draw a picture if you're…

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Q: Exercise 1. Prove that for sets A, B,C we have C \(AUB) = (C\ A) N (C \ B).

A: We have to show that for sets A, B, C   C ∖(A∪B)=(C∖A)∩(C∖B).

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

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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: Suppose that A and B are sets and f : A –→ B is a function. Fix subsets X,Y C A. Prove that Imf(X) –…

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Q: Determine (with argument) whether the following subsets of R are sub- spaces: 1. {(a, b, c) E R³ | a…

A: By Bartleby guidelines I can only answer the first three sub-questions. please repost the question…

Q: Find the cardinality of each of the following sets. a. A = {x:xe Z and x² = -9} b. B = {x:x € R and…

A: The given sets,(a) (b) (c) (d) The aim is to find the cardinality of each of the given sets.

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: Provide examples of sets A and B where strict inequality sup(A+B) < sup A+ sup B holds.

A: We have to given an example to prove given inequality:

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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