Please solve both part Prove: If AC [0, 1] and m* (A) > 0, then there exist x and y inProblem 1A such that x - y is an irrational number.Problem 2Prove: If ACR and r ER, thenm* (A\{r}) = m* (A).(Thus, removing a point from a set does not change the outer measure.)

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Prove: If AC [0, 1] and m* (A) > 0, then there exist x and y in Problem 1 A such that x - y) is an irrational number.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.CT: Test

Problem 3CT: To prove a theorem of the form "If P, then Q" by the indirect method, the first line of the proof...

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Question

Please solve both part

Prove: If AC [0, 1] and m* (A) > 0, then there exist x and y in
Problem 1
A such that x - y is an irrational number.
Problem 2
Prove: If ACR and r ER, then
m* (A\{r}) = m* (A).
(Thus, removing a point from a set does not change the outer measure.)

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