For sets A, B ⊆ R, let A + B = {a + b | a ∈ A, b ∈ B}. For closed sets A, B ⊆ R, A + B is not necessarily closed.

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

A:

Q: Prove that the set {a E R: a2 not equal to 6} is open.

A:

Q: True or false? For all sets A and B,  (A∪B)'=A'∪B' This can be determined by constructing a…

A:

Q: Use the following definition of compactness: KCR is compact if every open covering B of K has a…

A: Let us prove that the union of compact spaces is also compact.

Q: Prove: For all sets A, B and C, (AUB) - (CA) = AU (B-C).

A:

Q: For set A={9,10,11,12,13,14} and set B, the set of all natural numbers between 8 and 14 inclusive,…

A:

Q: Please answer letter D and E onlyyy.

A:

Q: Please answer a, c & h

A: The given sets are as follows. U=N=1,1,3,4,…A=x∈N| x≥7=7,8,9,…B=x∈N|x is odd=1,3,5,7,9,…C=x∈N|x is a…

Q: Exercise 2.16. Suppose that A and B are countably infinite sets. (A) Show that AUB is countably…

A: Suppose A and B are two countably infinite sets.  To prove that A∪B is also countably infinite.…

Q: 2.4.6. Show by example that it is possible for the union of infinitely many closed sets to be open,…

A: Let Fn be a closed set

Q: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

A:

Q: Find an example of a set A with |A| = 3 which contains only other sets and has the following…

A:

Q: Determine whether the given set is linearly independent.

A: We will check that given set is linearly independent or not using definition of linear independency.…

Q: Suppose that you have two sets, and you know that both sets are convex. Proven that the intersection…

A: convex set is a set of points such that, given any two points x,y in that set, the straight line…

Q: Is the set {(x1, x2) ∈ R2; 2x1+x2 ≥ 1} convex? Justify your objection.

A: Consider the set      S = {(x1, x2) ∈ R2 : 2x1 + x2 ≥ 1} Let, the points (x1, x2), (x3, x4) be in S.…

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

A:

Q: Suppose A and B are nonvoid, bounded, disjoint subsets of R. Mark all of the properties that must be…

A: A and B are nonempty bounded disjoint subset of ℝ

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: Let A and B be infinite sets that are uncountable. Do an and B have the same car finality as each…

A: Let A and B be infinite sets that are uncountable. Do A and B have the same cardinality as each…

Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

A:

Q: >) Recall that the symmetric difference of two sets X and Y, denoted XAY = (X-Y)U(Y-X), is the set…

A:

Q: If lim s₁ = s, then lim s² = s².

A: We have to prove if lim sn = s, then lim = s2, using epsilon-N method.

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: Let A, B, and C be sets. Prove that: Ax (B\C) = (A × B) \ (A × C).

A:

Q: If A p⊂ B, prove that if B is bounded, then A is also bounded. Is the converse true?

A: Note we consider A = A p Let A p⊂B, where B is bounded.

Q: Give a counterexample to show that the statement For all sets A, B and C, if A⊈BandB⊈C,thenA⊈C.…

A:

Q: (a) For all sets A, B, C, A × (BU C) = (A × B) U (A × C). (b) For all sets A and B, P(AUB) ≤ P(A)…

A:

Q: State whether each of the following statements are true or false. If the statement is false, rewrite…

A: Part (i) If Then Hence So given statement is wrong . The correct statement is If Then

Q: Suppose A and B are two finite sets such that |B| = 2 |A| and the number of relations on A is 16.…

A:

Q: Show that for every pair of sets X and Y, the sets X × Y and U {(x, y) | y ≤ Y} xEX are equal.

A:

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…

A:

Q: Let A E R2x3, be R². Determine whether or not S = {x R³ | Ax=b, x₁ ≤ 0, x₂ ≤ 0} X2 sa convex set.

A: