Question

c. which of the following describes the set of natural numbers greater than 95?
a. it is not well defined. it is not possible to list all of the natural numbers greater than 95
b. it is well defined. given a number, it is possible to tell whether it is a natural number
c. it is not well defined. there is no clear meaning of \greater than 95\
d. it is not well defined. there is no clear meaning of
atural numbers\
e. it is well defined. given a number, it is possible to tell whether it is a natural number greater than 95
f. it is well defined. it is possible to list all of the natural numbers greater than 95

Explanation:

To determine the correct description of the set of natural numbers greater than 95:

• A set is well - defined if for any element, we can clearly tell if it belongs to the set. For “natural numbers greater than 95”, given a number, we can check if it's a natural number and greater than 95 (so the set is well - defined).
• The set of natural numbers greater than 95 is infinite (e.g., 96, 97, 98,...), so we can't list all its elements.

Now let's analyze each option:

• Option A: Says the set is not well - defined (wrong, as we can determine membership) and that we can't list all elements (correct about listing, but wrong about well - defined).
• Option B: Says the set is well - defined (correct, as membership is clear) and that we can't list all elements (correct, since it's infinite).
• Option C: Says the set is not well - defined (wrong) and complains about “greater than 95” being unclear (but “greater than 95” is clear for natural numbers).
• Option D: Says the set is not well - defined (wrong) and complains about “natural numbers” being unclear (but “natural numbers” has a clear definition).
• Option E: Says the set is well - defined (correct) but claims we can tell if a number is in the set (which is true for well - definedness) but also implies we can list all elements (wrong, as it's infinite).
• Option F: Says the set is well - defined (correct) but claims we can list all elements (wrong, as it's an infinite set).

Answer:

B. It is well defined. Given a number, it is possible to tell whether it is a natural number greater than 95. It is not possible to list all of the natural numbers greater than 95