Question

List the element of, Z=[-4,6]n[0,8)
The elements in the intervals are all integers

Answer 1

To find the elements of the set \( Z = [-4, 6] \cap [0, 8) \) where all elements are integers, we first need to determine the individual intervals and their integer components:

1. The interval \( [-4, 6] \) includes all integers from -4 to 6:
\[
-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6
\]

2. The interval \( [0, 8) \) includes all integers from 0 to 7 (since 8 is not included):
\[
0, 1, 2, 3, 4, 5, 6, 7
\]

Next, we take the intersection of the two sets \( [-4, 6] \) and \( [0, 8) \):

The common integers in both sets are:
\[
0, 1, 2, 3, 4, 5, 6
\]

Thus, the elements of the set \( Z \) are:
\[
Z = \{ 0, 1, 2, 3, 4, 5, 6 \}
\]