Find the union of each of the following pairs of sets:
$A = \{ x : x \text{ is a natural number and } 1 < x \le 6 \}$
$B = \{ x : x \text{ is a natural number and } 6 < x < 10 \}$

First,represent the sets in roster form:
$A = \{ x : x \in \mathbb{N}, 1 < x \le 6 \} = \{ 2, 3, 4, 5, 6 \}$
$B = \{ x : x \in \mathbb{N}, 6 < x < 10 \} = \{ 7, 8, 9 \}$
The union of two sets $A$ and $B$,denoted by $A \cup B$,is the set of all elements which are in $A$ or in $B$.
$A \cup B = \{ 2, 3, 4, 5, 6, 7, 8, 9 \}$
In set-builder form,this can be written as:
$A \cup B = \{ x : x \in \mathbb{N} \text{ and } 1 < x < 10 \}$