8.I. Every open subset of R? is the union of a countable collection of sets which are closed. (Hint: the set of points all of whose coordinates are rational is countable.) 8.J. Every closed subset in R» is the intersection of a countable collection of sets which are onen.

Q: ieN (4 For each nEN, let A, = {-2n,0,2n}. (a) UA; = (b) NA: = ieN ieN

A:

Q: 2. Show that the limit set of the set of rational numbers, i.e. Q', is the set of real numbers R,…

A:

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

A:

Q: 2.4-Samantha Roth 8/29/2021 8. Describe the set by referring to the numbered regions. A-(BUC') 16 17…

A: Solution:-Given the venn diagram of a set U      By using this we need to find  A (BUC')

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

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

Q: 4) (AS) V (AST) = AAS, VS₂ SEA, S₂ € ₂

A: The given equation is  ∩s∈S1S∪∩s∈S2S=∩s2∈S2∩s1∈S1S1∪S2=∩s2∈S2S2∪∩s1∈S1S1 To prove the equality. The…

Q: 2. Using inclusion-exclusion find the number of words of length 10 in the letters A,B,C,D that do…

A:

Q: ☺ Let (u,Ue...,un) be a lineorly ndependent list. Which True Statement? is a has --- a non-zero…

A:

Q: A. Let A = {x ∈ N | x = y^2 such that y ∈ N and 2 ≤ y ≤ 7}     B = {x ∈ N | x = 5y, such that y ∈ N…

A:

Q: 9.T. Give an example of an open subset of R which is dense in RP. Can you give an example of a…

A: since the given set is universal one so it is itself an open and closed subset

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.