i) show that a closed interval is a closed set;

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

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Q: Provide a counter example that infinity intersection of open set is open

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Q: 1. Let A = [1, 3], B = (2, 5], and C= {2}. Write the inequalities (or equalities) that specify each…

A: We will just use of definitions of different type of sets

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: 1) Let the set S be defined as S = {x | x is a U.S. President} Find n(S). 2) Define compliment to a…

A: use the basic property of sets .

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: 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: Give an example of a bounded set that has infinitely many isolated points

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Q: Consider following five sets: I. { , } { } II. { } III. IV. { , , } V. { , } Find all linearly…

A: We have to check whether given set of vectors linearly independent or linearly dependent by known…

Q: I need help with this question It's about inequality notation.

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

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Q: Which of the following sets, given by the roster method, is equal to the set below given in…

A: The objective of the question is to find the set that matches the set-builder notation {x belongs to…

Q: Explain the idea of cardinality. When is a set denumerable? Show that the union of two denumerable…

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