Use bracket notation to give the set {n ∈ N | n > 3} - {n ∈ Z | n < 5} in a finite listed form.

Steps to Solve

1. Identify the sets involved

The first set is defined as $ { n \in \mathbb{N} | n > 3 } $, which consists of natural numbers greater than 3.

The second set is $ { n \in \mathbb{Z} | n < 5 } $, which consists of integers less than 5.

2. List the elements of the first set

The natural numbers greater than 3 are:

$$ {4, 5, 6, 7, 8, \ldots} $$

This set continues indefinitely with all natural numbers above 3.

3. List the elements of the second set

The integers less than 5 are:

$$ { \ldots, -2, -1, 0, 1, 2, 3, 4 } $$

This set contains all integers less than 5, including negative integers.

4. Subtract the second set from the first set

Now, we need to subtract the integers less than 5 from the natural numbers greater than 3.

Since the integers less than 5 include 4, we must remove it from the first set. The resulting set will be:

$$ { n \in \mathbb{N} | n > 3 } - { n \in \mathbb{Z} | n < 5 } = {5, 6, 7, 8, \ldots} $$

5. Express the final set in finite listed form

Since we typically express sets in finite notation, we can represent the final set containing just the first few elements:

$$ {5, 6, 7, 8, 9, \ldots} $$

But to provide a finite listing, we can write it as:

$$ {5, 6, 7, 8} $$