Determine whether the following sets are welldefined For ea

Determine whether the following sets are well-defined . For each well-defined set,state whether it is finite or infinite.
a)The set of all counties in Oregon that have a resident named James Smith
b)The set of well-written discrete math textbooks.
c)The set of differentiable functions from the unit interval to the real numbers.
d)The set of rational numbers between 1776 and 2016
e)The set of integers between 1776 and 2016 that contains the digits 0 and 4 but are not multiples of 3
f)The set of all rational numbers y such that y is greater than or equal to x.
g)The set of digits in the decimal expansion of pi
h)The set of all positive real numbers whose square is less than -2

Solution

(a) The set of all counties in Oregon that have a resident named James Smith.

Set is well defined and finite.

(b) The set of well-written discrete math textbooks.

Set is well defined and finite.

(c) The set of differentiable functions from the unit interval to the real numbers.

Set is well defined and infinite.

(There are infintie number of functions from unit interval to the real numbers.)

(d) The set of rational numbers between 1776 and 2016.

The set is well defined and infinite because there are infinite number of rational numbers between 1776 and 2016.

(e) The set of integers between 1776 and 2016 that contains the digits 0 and 4 but are not multiples of 3.

The set is well defined and finite.

(f) The set of all rational numbers y such that y is greater than or equal to x.

The set is well defined and infinite.

(g) The set of digits in the decimal expansion of pi.

The set is well defined and infinite.

(h) The set of all positive real numbers whose square is less than -2.

The set is not well defined since square of positive real number is never negative.