Alright, let's break this problem down step-by-step.
### (a) {x: x is an even number; x < 8}
We are asked to list all the even numbers that are less than 8.
1. Identify the even numbers between 0 and 7 (since x < 8). These numbers will be those that are divisible by 2 without leaving a remainder.
2. The even numbers in this range are:
- 0 (because 0 % 2 == 0)
- 2 (because 2 % 2 == 0)
- 4 (because 4 % 2 == 0)
- 6 (because 6 % 2 == 0)
Therefore, the set can be described as follows:
[tex]\[
\{ x \mid x \text{ is an even number and } x < 8 \} = \{ 0, 2, 4, 6 \}
\][/tex]
### (b) {x: x is an English vowel letter}
We need to list all the English vowel letters. The English alphabet has both uppercase and lowercase vowels.
1. The English vowels in uppercase letters are:
- 'A', 'E', 'I', 'O', 'U'
2. The English vowels in lowercase letters are:
- 'a', 'e', 'i', 'o', 'u'
Combining both uppercase and lowercase vowels together, we get:
[tex]\[
\{ x \mid x \text{ is an English vowel letter} \} = \{ 'A', 'E', 'I', 'O', 'U', 'a', 'e', 'i', 'o', 'u' \}
\][/tex]
Putting both sets together, the results are:
### Final Sets
(a) \{0, 2, 4, 6\}
(b) \{ 'A', 'E', 'I', 'O', 'U', 'a', 'e', 'i', 'o', 'u' \}
These are the sets based on the given descriptions.
