Question

determine if the collection is not well defined and therefore not a set.
the collection of natural numbers greater than one quadrillion

choose the correct answer below.

a. the collection is well defined and is therefore a set because the contents of the collection cannot be clearly determined.

b. the collection is not well defined and is therefore not a set because the contents of the collection cannot be clearly determined.

c. the collection is not well defined and is therefore not a set because the contents of the collection can be clearly determined.

d. the collection is well defined and is therefore a set because the contents of the collection can be clearly determined.

Explanation:

To determine if a collection is a set, it must be well - defined, meaning we can clearly decide if an element belongs to it. The collection of natural numbers greater than one quadrillion: we know that a natural number is a positive integer (1, 2, 3, ...). For any given number, we can clearly check if it is greater than one quadrillion. So the contents of this collection can be clearly determined, which means the collection is well - defined and thus a set. Now let's analyze the options:

• Option A: Says the collection is well - defined but gives the wrong reason (says contents cannot be clearly determined). Eliminate A.
• Option B: Says the collection is not well - defined, which is wrong. Eliminate B.
• Option C: Says the collection is not well - defined and gives a wrong reason (says contents can be clearly determined but claims it's not well - defined). Eliminate C.
• Option D: Correctly states that the collection is well - defined (because we can clearly determine if a number is a natural number greater than one quadrillion) and thus is a set.

Answer:

D. The collection is well defined and is therefore a set because the contents of the collection can be clearly determined.