Problem 32 - College Algebra Essentials

Question

Find the union of the sets. $$\\{0,1,3,5\\} \cup\\{2,4,6\\}$$

Step-by-Step Solution

Answer

The union of the sets \( \{0,1,3,5\} \) and \( \{2,4,6\} \) is \( \{0,1,2,3,4,5,6\} \).

Step 1: Identify Elements in First Set

The first set includes the elements \( \{0,1,3,5\} \).

Step 2: Identify Elements in Second Set

The second set includes the elements \( \{2,4,6\} \).

Step 3: Combine All Unique Elements

The union of these two sets, denoted by \( \cup \), is all the unique elements from both sets. This means combining both sets of elements and listing them once, regardless if they appeared in both set 1 and set 2. In this case, none of the elements are repeated in either set. This operation results in \( \{0,1,2,3,4,5,6\} \).