In this question, we show the following: Let ECR, and a < b real numbers. If every point in the open interval (a, b) is a limit point of E, then a and b are also limit points of E. (In this question, we only consider a. The proof for b works identically.) (a) Write the hypothesis "every point in the open interval (a, b) is a limit point of E" as a statement in formal mathematical language.

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Q: 6. Show that the span of this set is all of R?. {}}

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A: In this question, we show the following: Let E  . and a &lt; b real numbers. If every point in the…

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A: use the basic property of sets .

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A: (a) Consider here      Noted that here  are limit points of  .Because here if write the some…

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Q: Let (5,}nen is a disjoint segeuence of measurable sets , then: H(S) ulgn

A: Ans : true , because

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A: The detailed solution is as follows below:

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A: We need to prove the above theorem.

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A: If E is a measurable set, then each translate E+y of E is also measurable.

Q: 3. Let a, b e R such that a < b. Prove that the open interval (a, b) is an open set in R.

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