Problem 30 - Algebra and Trigonometry

Question

Find the union of the sets. $$\\{1,3,7,8\\} \cup\\{2,3,8\\}$$

Step-by-Step Solution

Answer

The union of the two sets is \(\{1,2,3,7,8\}\)

Step 1: Identifying elements in each set

The first step is to identify and list down the elements in each set. The first set \(\{1,3,7,8\}\) has the elements 1, 3, 7, 8. And the second set \(\{2,3,8\}\) has the elements 2, 3, 8. It is noted that the elements 3 and 8 exist in both sets.

Step 2: Combining the elements

The second step is to combine the elements from both sets into a new set. This new set will have all the elements from both sets, but without any repetitions. It means that the elements 3 and 8 which exist in both sets should be listed only once. Therefore, the elements in the new set are 1, 2, 3, 7, 8.

Step 3: Writing the Final Answer

The final step is to write down the final answer. The answer is the new set containing all the distinct elements from both sets, i.e. \( \{1,2,3,7,8\} \).