Question

which of the following describes the set of whole numbers greater than 175? a. it is well defined. given a number, it is possible to tell whether it is a whole number. b. it is not well defined. it is not possible to list all of the whole numbers greater than 175. c. it is well defined. it is possible to list all of the whole numbers greater than 175. d. it is well defined. given a number, it is possible to tell whether it is a whole number greater than 175. e. it is not well defined. there is no clear meaning of greater than 175. f. it is not well defined. there is no clear meaning of whole numbers.

Explanation:

To determine the set of whole numbers greater than 175: A set is well - defined if for any element, we can clearly determine if it belongs to the set. For a number, we can check if it's a whole number and greater than 175 (so well - defined). Also, the set of whole numbers greater than 175 is infinite, so we can't list all elements. Option D says "It is well defined. Given a number, it is possible to tell whether it is a whole number greater than 175" which matches. Option A: We can't list all whole numbers >175 (infinite), so A is wrong. Option B: The set is well - defined, so B is wrong. Option C: Can't list all (infinite), so C is wrong. Options E, F: The set is well - defined (clear criteria), so E, F are wrong.

Answer:

D. It is well defined. Given a number, it is possible to tell whether it is a whole number greater than 175.