Find the union of each of the following pairs of sets:
$A = \{ x : x \text{ is a natural number and a multiple of } 3 \}$
$B = \{ x : x \text{ is a natural number less than } 6 \}$
$A = \{ x : x \text{ is a natural number and a multiple of } 3 \}$
$B = \{ x : x \text{ is a natural number less than } 6 \}$
(N/A) $A = \{ x : x \text{ is a natural number and a multiple of } 3 \} = \{ 3, 6, 9, 12, \ldots \}$
$B = \{ x : x \text{ is a natural number less than } 6 \} = \{ 1, 2, 3, 4, 5 \}$
$A \cup B = \{ 1, 2, 3, 4, 5, 6, 9, 12, \ldots \}$
$\therefore A \cup B = \{ x : x = 1, 2, 4, 5 \text{ or } x \text{ is a multiple of } 3 \}$
$B = \{ x : x \text{ is a natural number less than } 6 \} = \{ 1, 2, 3, 4, 5 \}$
$A \cup B = \{ 1, 2, 3, 4, 5, 6, 9, 12, \ldots \}$
$\therefore A \cup B = \{ x : x = 1, 2, 4, 5 \text{ or } x \text{ is a multiple of } 3 \}$
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