By considering the collection of intervals {(-) : n € N} show that the intersection of an infinite number of open sets need not be open.

Q: Suppose A and B are bounded non-empty sets of real numbers. Prove sup ( (AUB) max & Sup A sup Bee or…

A:

Q: Show that R has the same cardinality as the interval (–2, 2) by building a bijection between the two…

A: This is a problem of Real Analysis and Topology.

Q: Let A be a set with |A| = n. Using induction, prove that |P(A)| = 2^n .

A: To show that the cardinality of power set of A is 2n when given that cardinality of A is n.

Q: Show that a nonempty set has the same number of odd subsets (i.e., subsets with an odd number of…

A: To Show- Show that a nonempty set has the same number of odd subsets (i.e., subsets with an odd…

Q: 6) If X is N(45,5) for i = 1, 2,..., 25; find: 25 (a) P (30 < (X-45) < 55) 221 b) P(30< (X -45) 2 <…

A: The objective of the question is to find the probability of two different scenarios for a normally…

Q: Let X be the set comprising all numbers of the following two types: • Natural numbers; • Natural…

A: From (i) &amp; (ii), we conclude that the function f is well defined.

Q: What set is in another class of infinity that is bigger than N?

A: We know that N represents set of natural number which is countably infinite. In order to get set…

Q: Prove that for all divides natural numbers nt 7^-2^.

A:

Q: {m belongs to all integers| m^2=3}    Now list the elements in the set?

A: The given set is {m belongs to all integers| m2=3}.To list down the elements in the given…

Q: a Prove that the interval [-1, 2] is a closed set in R. Explain each step in your argument.

A:

Q: Create three non-empty sets A, B, C, that show this statement is FALSE: For all sets A, B, C: A- (Bn…

A:

Q: A = {x € Z: xis even} {91'SI'ZI'6'S'E} = 5 23242+3 2184 21+ 122198 th

A: Given,            To find the value of

Q: Determine in set notation where Continuas nuuas S! x^~X + E =X)

A: Given , f(x) = 3 + x2 - √x We have to determine where the function is continuous

Q: Let A = {7, 11, 29, 54, 72, 83). Find the set denoted by {[]: € A}.

A:

Q: Is the set (9, 20] under usual order ≤ well-ordered? Why?

A: We need to determine the set (9 , 20] under usual order is well - ordered or not. We know that , a…

Q: 5. Show that a finite set is a closed set.

A:

Q: VI.[15] Let the Universal set be the set R, of all real numbers. [ Hint: Use real number line to…

A: a). Here A = {x € R |  -3 &lt; x &lt; 0} B = {x € R |  -1 &lt; x &lt; 2} A U B contains all the…

Q: not Show that Ris Aft connected surgen fray half opon interval topology the

A: We need to show that ℝ is not connected in the Sorgenfrey half-open interval topology. A connected…

Q: 2 16 List the elements of the set 4, V25, 2.3, V7, -1} that are also elements of 3 2 each given set.…

A: