(c) The set of all straight lines in the Cartesian plane, each of which passes through the origin and a point having both coordinates rational. (d) The set of all intervals on the real line having both endpoints rational. (e) Any infinite set of nonoverlapping intervals on the real line. - Prove that the

Advanced Engineering Mathematics
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10 a,b,c,d,e

(c) The set of all straight lines in the Cartesian
plane, each of which passes through the origin
and a point having both coordinates rational.
(d) The set of all intervals on the real line having
both endpoints rational.
(e) Any infinite set of nonoverlapping intervals on
the real line.
- Prove that the
Transcribed Image Text:(c) The set of all straight lines in the Cartesian plane, each of which passes through the origin and a point having both coordinates rational. (d) The set of all intervals on the real line having both endpoints rational. (e) Any infinite set of nonoverlapping intervals on the real line. - Prove that the
10. Determine whether each of the following sets is
countable or uncountable:
(a) The set of all numbers of the form m/2", where
m is an integer and n is a natural number.
(b) The set of all straight lines in the Cartesian
plane, each of which passes through the origin.
Transcribed Image Text:10. Determine whether each of the following sets is countable or uncountable: (a) The set of all numbers of the form m/2", where m is an integer and n is a natural number. (b) The set of all straight lines in the Cartesian plane, each of which passes through the origin.
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