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Chapter 9: Problem 37

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

Short Answer

Expert verified
The union of the sets \(\{a, e, i, o, u\} \cup \varnothing\) is \(\{a, e, i, o, u\}\).

Step by step solution

01

Identify the Sets

The first step is to identify the two sets that we're dealing with. The first set is \(\{a, e, i, o, u\}\), representing the vowels, and the second set is \(\varnothing\), the empty set.
02

Understand Union of Sets

The union of two sets A and B, denoted by A 鈭� B, is the set of elements which are in A, in B, or in both A and B. In simpler terms, it's a set that includes all the unique elements from both sets.
03

Find the Union of Given Sets

Since set two is an empty set, the union of the two sets would yield the elements of the first set, because there are no elements in the second set. Therefore, the union of the two sets, \(\{a, e, i, o, u\} \cup \varnothing\), would be the set \(\{a, e, i, o, u\}\).

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