Select all of the following true statements if R = real numbers, N = natural numbers, and W = {0, 1, 2, ...}.

This question needs a set of statements to select the right ones. I wonder why you did not include the statements.

I did a little of research and found these statements as the choices of this question:

a) - 5 ∈ W
b) r ⊂ W
c) {0,1,2,...} ⊂ N
d) ∅ ⊂ N
e) 9 ∈ W
f) W ⊂ N

Answer:

c) d) f) and e) are the correct ones.

Explanation:

a) FALSE: - 5 is not an element of W becasue has only positive integer numbers and 0.

b) FALSE: r is not a subset of W because the real numbers, R, is much bigger than W, this is R include negative numbers, zero, positive numbers, rational numbers (fractions), and irrational numbers.

c) TRUE: {0,1,2,...} is the same set W and it is a convention that any set is a subset of itself, so this is TRUE.

d) TRUE: the empty set is a subset of any set.

e) TRUE: 9 is natural number, i.e. it is an element of N

f) TRUE: W is a subset of N, because W is the same set N.

That is the answer if your statements are the same that I found. Any how, my list is pretty comprenhensive so this explanation must be enough to understand most cases.