Problem 33 - College Algebra Essentials

Question

Find the union of the sets. $$\\{a, e, i, o, u\\} \cup \varnothing$$

Step-by-Step Solution

Answer

The union of the sets \{a, e, i, o, u\} and \varnothing is \{a, e, i, o, u\}

Step 1: Identify the Sets

First, identify the two sets. The first set is \{a, e, i, o, u\}, which is the set of English vowels. The second set is \varnothing, which is an empty set, a set with no elements.

Step 2: Understand the Union Operation

Next, understand what the union of two sets is. The union of two sets A and B, denoted by A \cup B, is the set of elements that are in A, in B, or in both A and B.

Step 3: Apply the Union Operation

Finally, apply the union operation to the given sets. Since the second set is an empty set, adding its non-existent members to the first set doesn't change the first set. Therefore, the union of the given sets is simply the first set of English vowels, \{a, e, i, o, u\}