Let A be the set of all constant sequences in R^N. Prove that A is a closed set relative to the box topology.  Note: Show that the complement of A is open.

Q: Show that the space (P is complete.

A: The given problem is to show that the space lp is complete. we can use properties of lp spaces to…

Q: 6. Show that the span of this set is all of R?. {}}

A: Let S=v1,v2,...,vn be a set of vectors in a vector space V(F) . The vector space V is spanned by S,…

Q: Consider the partial order with domain{3,5,6,7,10,14,20,30,60}and with x ≤ y if x evenly divides y.…

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Q: ABCD Y 0000 1 0001 X 0010 1 0011X 0100 0101 . 1 0110 1 0111 1000 1001 1010 1 1011 1100 1101 1 1110…

A: fA,B,C,D=∑i=116 ki=1 , i∈1,3,6,7,11,14=minitermsfA,B,C,D=∑i=116 hi=0 ,…

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: Use graph to find  set. [1, 3) ∩ (0, 4)

A: Given set is  [1, 3) ∩ (0, 4) The graph of the given set is as shown

Q: Prove that (2,5) is an open set

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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) ^…

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

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Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

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Q: (a) |z – 1+ il 1

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Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

Q: Let A be a partially ordered set that has the least upper bound property. Then every nonempty subset…

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Q: Consider two sets A and B such that A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Find the set C…

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Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

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Q: Q.No.2 Let X be a universal set and A, B be the subsets of X.Then prove the following. (a) ((A*…

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Q: Problem 4: Find a recurrence relation for the numbers F(n) in terms of F(i), where i < n. Here F(n)…

A: Our  objective is to find the recurrence relation.

Q: 3. Determine if the set Q n (0,1) is open, closed or neither. What is the boundary of the set? Also…

A: 1. Q ∩ (0,1) is neither open nor closed. 2. For the set Q ∩ (0,1), the boundary includes the points…

Q: 1. Show that 2 is a primitive root modulo 13. 2. For each element a in T, find the index of a mod 13…

A: T=1,2,3,4,5,6,7,8,9,10,11,12

Q: Use graph to find set. [2, ∞)∩ (4, ∞)

A: Use the graph to find [2,∞)∩(4,∞)

Q: is the set [5,100] compact?

A: Given that:A set is S=5,100.We have to check whether a set 5,100 is compact or not?

Q: how that the union of a finite. number of bounded sets is bounded

A: A statement is given as, 'the union of a finite number of bounded sets is bounded. The objective is…

Q: et A be the set of letters in the English alphabet with the usual order. Define (A², <) such that…

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Q: Let A = {0, 1, 2} and let B = {-2, 0, 1, 2}. %3D

A: Given,        A=0, 1, 2, and B=-2, 0, 1, 2

Q: Write out the elements of the set 2X where X= = {1,{0}, Ø, {2,3}}.

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Q: List all the ordered pairs in the relation R= {(a, b) | gcd(a,b) = 1} on the set {2, 3, 4, 5, 6}.

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