Questions: Find the number of elements in the following sets. Complete parts (a) and (b) below. a. x x is a letter in the word inconcoction square elements b. The set of letters appearing in the word disinterestedness. square elements

Find the number of elements in the following sets. Complete parts (a) and (b) below. a. x x is a letter in the word inconcoction square elements b. The set of letters appearing in the word disinterestedness. square elements
Transcript text: Find the number of elements in the following sets. Complete parts (a) and (b) below. a. $\{x \mid x$ is a letter in the word inconcoction $\}$ $\square$ elements b. The set of letters appearing in the word disinterestedness. $\square$ elements
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Solution

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Solution Steps

To find the number of elements in a set of letters from a word, we need to identify the unique letters in the word. This can be done by converting the word into a set, which automatically removes duplicates, and then counting the number of elements in the set.

Step 1: Unique Letters in "inconcoction"

To find the number of unique letters in the word "inconcoction", we identify the distinct letters present. The unique letters are \( \{c, n, t, o, i\} \). Therefore, the number of elements in this set is given by:

\[ | \{x \mid x \text{ is a letter in the word inconcoction} \} | = 5 \]

Step 2: Unique Letters in "disinterestedness"

Next, we analyze the word "disinterestedness" to determine its unique letters. The distinct letters are \( \{s, n, t, e, d, i, r\} \). Thus, the number of elements in this set is:

\[ | \{x \mid x \text{ is a letter in the word disinterestedness} \} | = 7 \]

Final Answer

The number of unique letters in "inconcoction" is \( \boxed{5} \) and in "disinterestedness" is \( \boxed{7} \).

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