Find the union of each of the following pairs of sets:
$A = \{ x : x \text{ is a natural number and } 1 < x \le 6 \}$
$B = \{ x : x \text{ is a natural number and } 6 < x < 10 \}$
$A = \{ x : x \text{ is a natural number and } 1 < x \le 6 \}$
$B = \{ x : x \text{ is a natural number and } 6 < x < 10 \}$
(A) First,we list the elements of set $A$:
$A = \{ x : x \in \mathbb{N}, 1 < x \le 6 \} = \{ 2, 3, 4, 5, 6 \}$
Next,we list the elements of set $B$:
$B = \{ x : x \in \mathbb{N}, 6 < x < 10 \} = \{ 7, 8, 9 \}$
The union of two sets $A$ and $B$,denoted by $A \cup B$,is the set of all elements which are in $A$,in $B$,or in both.
$A \cup B = \{ 2, 3, 4, 5, 6, 7, 8, 9 \}$
$A = \{ x : x \in \mathbb{N}, 1 < x \le 6 \} = \{ 2, 3, 4, 5, 6 \}$
Next,we list the elements of set $B$:
$B = \{ x : x \in \mathbb{N}, 6 < x < 10 \} = \{ 7, 8, 9 \}$
The union of two sets $A$ and $B$,denoted by $A \cup B$,is the set of all elements which are in $A$,in $B$,or in both.
$A \cup B = \{ 2, 3, 4, 5, 6, 7, 8, 9 \}$
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