For each integer n, denote by Cn the set of all real numbers less than n, and fo

Question

For each integer n, denote by Cn the set of all real numbers less than n,

and for each positive number n let Dn be the set of all real numbers less

than 1/n. Express each of the following unions or intersections in a

simpler way. For example, the answer to (a) is C10. The answer is not

always one of the sets Ci or Di , but there is an equally simple answer in

each case. Since infinity is not a number, the expressions C** and D** do not

make sense and should not appear in your answers.

a.{Cn | 1 <= n <= 10} = C10

b.{Dn | 1 <= n <= 10} = D1

c.{Cn | 1 <= n <= 10}= C1

d.{Dn | 1 <= n <= 10}= D10

e.{Cn | 1 <= n} = R

f.{Dn | 1 <= n} = D1

g.{Cn | 1 <= n} = C1

http://www.chegg.com/homework-help/integer-n-denote-cn-set-real-numbers-n-positive-number-n-let-chapter-1-problem-9-solution-9780073191461-exc

Can someone explain to me how these answers came about in more depth than the answer guide does. I need seeing what is happening for these answers to come about. Explaining one or two should be enought. Thanks in advance.

Explanation / Answer

For Cn you donot need to worry.

Just try to understand the concept of Union and intersection.

Now, If you have n = [1, 10] n belongs to integer

C(n) = [1, n] where n less than 10 and belongs to real number.

C(10) = 0.1, 1.0, 2.0 , 2.56 etc all real numbers.

D(10) = less than 0.1 means 0.001, 0.002 etc.

Now take union of these two. and try to have answer. than proceed same for intersection. I am leaving it to you :)

If furthur any doubt you can mail me on ashishkguptaiit.cse@gmail.com

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