Question 2* Which one of the followings is compact a. A discrete space with at least to points. b. Any set with the trivial topology. c. R with the usual topology. d. None of the above.

Q: Vhich of the following sets is a null set ? I. X {x | x= 9, 2x = 4 } II. Y {x | x= 2x, x #0 } III.…

A:

Q: 1. example of sets A and B for which A B but Ag B.

A: Cardinality of a set is number of elements in the set.

Q: Let A and B be sets. Prove that A U B = An B if and only if A = B

A: First show if A∪B=A∩B then A=B, then show that if A=B then we have A∪B=A∩B.

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: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: Q14D. Define the sets A, B, C, and D as follows: A = {-3, 1, 6, 7, 10} B = {-10, -5, 1, 4, 6} C =…

A: Given:A=-3,1,6,7,10B=-10,-5,1,4,6C=x∈Z : x is oddD=x∈Z : x is positive To find: A∩D Also, express…

Q: Let A and B be finite sets with A - B = {a, b, c, d, e, f, g} and An B = {h, i, j, k, l, m}. Find…

A:

Q: When is a set compact?

A:

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

A:

Q: Which of the following pairs of sets can be placed in a one-to-one correspondence? Why? (a) { a, b,…

A:

Q: Let ∅ be the empty set. Let X be the real line, the entire plane, or, in the three-dimensional case,…

A: Given:

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: 2. Let A = notation. {a,b,c}, B = {1,2}, C = {X, Y}. Write out the indicated set in list (A x B) x C

A: For given A, B, C set we have to find the value of (A x B) x C.

Q: Which sets are compact? The union of [0, 1] and [2, 3]

A: Concepts introduction: Theorem (Heine-Borel Theorem): A subset S of R is compact if and only if S is…

Q: Let ?1and ?2 be compact subsets of a metric space X. Show ?1 ∪ ?2 is compact

A:

Q: Proposition 1.35. The intersection of any family of closed sets in a metric space X is also closed…

A:

Q: A, B be subsets of a metric space. Show that A U B = B and that A B. Give an example to show that An…

A:

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: Question 1. Let X and Y be infinite sets. Let X be equipped with the discrete topology, and Y…

A: Given, X and Y be two infinite sets in topological space.  X is a discrete topology and Y is a…

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: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

Q: If S1 and S2 are convex sets, prove that their intersection S1 N S2 is also a convex set.

A:

Q: 10. The set {0} in the indiscrete space X is A.open but not closed B.closed but not open C.both open…

A:

Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

A: