Questions: List the elements of the set in roster notation. (Enter EMPTY or ø for the empty set.) x x is a letter in the word HIPPOPOTAMUS State whether the statements are true or false. (a) a, b, c=c, a, b

List the elements of the set in roster notation. (Enter EMPTY or ø for the empty set.) x x is a letter in the word HIPPOPOTAMUS State whether the statements are true or false. (a) a, b, c=c, a, b
Transcript text: List the elements of the set in roster notation. (Enter EMPTY or ø for the empty set.) $\{x \mid x$ is a letter in the word HIPPOPOTAMUS \} State whether the statements are true or false. (a) $\{a, b, c\}=\{c, a, b\}$
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Solution

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Solution Steps

Solution Approach

  1. For the first question, we need to identify the unique letters in the word "HIPPOPOTAMUS" and list them in roster notation. This involves converting the word into a set to automatically handle duplicates and then listing the elements.

  2. For the second question, we need to determine if the two sets are equal. Two sets are equal if they contain exactly the same elements, regardless of the order.

Step 1: Identify Unique Letters

The unique letters in the word "HIPPOPOTAMUS" are determined by forming the set \( \{x \mid x \text{ is a letter in the word HIPPOPOTAMUS}\} \). The unique letters are \( \{T, S, U, P, I, O, M, H, A\} \).

Step 2: List in Roster Notation

The elements of the set in roster notation are \( \{T, S, U, P, I, O, M, H, A\} \).

Step 3: Check Set Equality

To determine if the sets \( \{a, b, c\} \) and \( \{c, a, b\} \) are equal, we find that both sets contain the same elements. Therefore, \( \{a, b, c\} = \{c, a, b\} \) is true.

Final Answer

The unique letters in roster notation are \( \{T, S, U, P, I, O, M, H, A\} \) and the statement about the sets is true. Thus, the answers are:

  • Unique letters: \( \boxed{\{T, S, U, P, I, O, M, H, A\}} \)
  • Set equality: \( \boxed{\text{True}} \)
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