Question

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

Answer 1

choices:
W c Z
R c W
0 E Z
∅ c R
{0, 1, 2, ...} c_ W
-2 E W

Answer 2

quick notation review:
A ⊂ B: A is a subset of B (every item in A is also in B)
A ∈ B: A is an element of B (the item A is included inside B)
∅: null set (an empty set)
A ⊆ B: A is a subset that can also be equal to B

simply go through the statements and evaluate whether they are true or false. I will not do all of them but I will do a few to help you get started.

W ⊂ Z: Z is the set of *all* integers, and W is the set of all integers starting with 0. therefore, every item in W is also included in Z, making this statement true.

0 ∈ Z: 0 is an integer, and since Z includes all integers, 0 is an element in Z. true statement.

repeat with the other statements, evaluating whether the statement is true based on the set definitions