Problem 32 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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

Step 1: Identify the given sets

The given sets are \(\{0,1,3,5\}\) and \(\{2,4,6\}\).

Step 2: Write down all elements from the first set

Write down all the elements from the first set. So, our resulting set contains these elements until now: \(\{0,1,3,5\}\).

Step 3: Add the elements from the second set

Add the elements from the second set to our resulting set, taking care not to repeat any elements that have been already included. But since there are no common elements between the two given sets, all elements of the second set are added to the resulting set: \(\{0,1,3,5\}\) \(\cup\) \(\{2,4,6\}\) = \(\{0, 1, 2, 3, 4, 5, 6\}\).