Question

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

a) -2 ∈ W
b) 0 ∉ CR
c) W ⊂ Z
d) [0, 1, 2, ...) ⊆ CW

Answer 1

The true statements are: b) and c). In this question, we are asked to determine which statements are true regarding sets and numbers. After analyzing each statement, we find that b) and c) are true.

Step-by-step explanation:

In the given question, we are asked to select all of the true statements among the given options. Let's analyze each option:

a) -2 ∈ W: This statement is false because -2 is not included in the set W, which consists of non-negative integers starting from 0.

b) 0 ∉ CR: This statement is true because 0 is not an element of the set of complex numbers (C).

c) W ⊂ Z: This statement is true because the set of non-negative integers (W) is a subset of the set of integers (Z), as every element in W is also an element of Z.

d) [0, 1, 2, ...) ⊆ CW: This statement is false because the notation CW is not well-defined. It seems to represent complex numbers with imaginary part belonging to the set W, but the set W only consists of non-negative integers, so there can't be any complex numbers in CW.

Therefore, the true statements are: b) and c).