Suppose is a family of sets such that for all i, ifthen (Such a family is called a

Chapter 2, Problem 16

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QUESTION:

Suppose is a family of sets such that for all i, ifthen (Such a family is called a decreasing nested family of sets.)(a) Prove that for every(b) Prove that

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QUESTION:

Suppose is a family of sets such that for all i, ifthen (Such a family is called a decreasing nested family of sets.)(a) Prove that for every(b) Prove that

ANSWER:

Problem 16

Suppose is a family of sets such that for all , if  then  (Such a family is called a decreasing nested family of sets.)

(a) Prove that for every  

(b) Prove that

                                                            Step-by-step solution

Step 1 of 3

Lemma: Let  be a non empty family of sets .

If  for every  then .

                                                              

If  for every  then

                                                     

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