To determine the cardinality of the set \( F \) defined by the expression \( F = \{ x \mid x \text{ is a letter in the word "elephant" } \} \), follow these steps:
1. Identify the Elements: List out all the letters in the word "elephant":
[tex]\[
\text{e, l, e, p, h, a, n, t}
\][/tex]
2. Eliminate Duplicates: Remove any repeating letters to form a set of unique letters:
[tex]\[
\{ \text{e, l, p, h, a, n, t} \}
\][/tex]
3. Count the Unique Elements: Determine the number of unique letters in the set.
Counting the elements in the set \( \{ \text{e, l, p, h, a, n, t} \} \), we get:
[tex]\[
e, l, p, h, a, n, t
\][/tex]
There are 7 unique letters.
Thus, the cardinality \( n(F) \) is:
[tex]\[
n(F) = 7
\][/tex]
So, the cardinality of the set [tex]\( F = \{ x \mid x \text{ is a letter in the word "elephant" } \} \)[/tex] is [tex]\( 7 \)[/tex].
