Problem 1 Set concepts State whether each of the following s

Problem 1 [Set concepts State whether each of the following sets is countable or uncountable, and finite or infinite B (the null set) C tz+t set of all positive integers D {Students enrolled at MSUY LE Athletes attending East Lansing High School F IStudents in the classrooms of East Lansing High School at 3:00 a.m., Sunday August 30, 2015 G {All possible length values less than 1 meter H tz -25 S ar S-3 (Read this as \"the set of all values of r such that is -25, but S-3 fr -2, -1, 1 2 Problem 2 Power set (used as an event space) Consider the sample space associated with a random experiment, given by S {a, b, c, d) (a) List every possible subset, that is, list the power set, say of S. Call the power set T. The power set of S is sometimes denoted 2 (b) (Extra credit easy, but blue-lined material in notes.) Suppose that we are told that the probability space involving S has an event space 3 that is not necessarily the power set of S. We are also told that a E 3 (the point set at is an event in F). What other events must be in and which ones need not be given this information?

Solution

A is a countable finite set , since A has one element and is finitie

B is countable finite set , B has one element hence countable and is finite

C is countable as number of elements can be counted and is infinite

D is countable as number of students enrolled is a countable value and is finite aas each university accepts only limited number of students

similarly E is countable and finite

similarly F is countable finite

G is uncountable infinite as there can be infinite values which are less than 1 m

H is uncountable as number of elements in set x are not known and is finite

I is countable and finite as only two elements present in the set no matter the values of x in domain

2)

Power set of S is
{
phi , (a,b,c,d) , (a), (b) , (c) , (d) , (a,b) , (a,c) , (a,d) , (b,c) , (b,d) , (c,d) , (a,b,c) , (a,c,d) , (b,c,d) , (a,b,d)
}

where phi is the null set