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QUESTION 5 Consider the following statements: (i) There exists a function f: R→ R that is discontinuous at every rational number and continuous at every irrational number. (ii) There exists a function f:R→R that is continuous and such that f(R) = Q. Which statements are true? Only (ii) is true. O Only (i) is true. Both are true. Neither are true.

QUESTION 5 Consider the following statements: (i) There exists a function f: R→ R that is discontinuous at every rational number and continuous at every irrational number. (ii) There exists a function f:R→R that is continuous and such that f(R) = Q. Which statements are true? Only (ii) is true. O Only (i) is true. Both are true. Neither are true.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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QUESTION 5 Consider the following statements: (i) There exists a function f: R→ R that is discontinuous at every rational number and continuous at every irrational number. (ii) There exists a function f:R→R that is continuous and such that f(R) = Q. Which statements are true? Only (ii) is true. O Only (i) is true. Both are true. Neither are true.
Transcribed Image Text:QUESTION 5 Consider the following statements: (i) There exists a function f: R→ R that is discontinuous at every rational number and continuous at every irrational number. (ii) There exists a function f:R→R that is continuous and such that f(R) = Q. Which statements are true? Only (ii) is true. O Only (i) is true. Both are true. Neither are true.
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