Questions: Let U=1,2,3, ..., 10, A=1,3,5,7, B=1,2,3,4, and C=3,4,6,7,9. Select A^c from the choices below. 4,5,6,7,8,9 1,2,4,5,6,8 2,3,4,7,8,10 2,4,6,8,9,10 1,2,3,6,7,9

Let U=1,2,3, ..., 10, A=1,3,5,7, B=1,2,3,4, and C=3,4,6,7,9. Select A^c from the choices below. 4,5,6,7,8,9 1,2,4,5,6,8 2,3,4,7,8,10 2,4,6,8,9,10 1,2,3,6,7,9
Transcript text: Let $U=\{1,2,3, \ldots, 10\}, A=\{1,3,5,7\}, B=\{1,2,3,4\}$, and $C=\{3,4,6,7,9\}$. Select $A^{c}$ from the choices below. $\{4,5,6,7,8,9\}$ $\{1,2,4,5,6,8\}$ $\{2,3,4,7,8,10\}$ $\{2,4,6,8,9,10\}$ $\{1,2,3,6,7,9\}$ $\emptyset$ Next Question
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Solution

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Solution Steps

Step 1: Determine the Complement of Set \( A \)

The complement of set \( A \), denoted \( A^c \), consists of all elements in the universal set \( U \) that are not in \( A \).

Given:

  • \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \)
  • \( A = \{1, 3, 5, 7\} \)

To find \( A^c \), we subtract the elements of \( A \) from \( U \):

\[ A^c = U - A = \{2, 4, 6, 8, 9, 10\} \]

Step 2: Match the Result with the Given Choices

We need to find which of the given choices matches \( A^c = \{2, 4, 6, 8, 9, 10\} \).

The choices are:

  • \(\{4,5,6,7,8,9\}\)
  • \(\{1,2,4,5,6,8\}\)
  • \(\{2,3,4,7,8,10\}\)
  • \(\{2,4,6,8,9,10\}\)
  • \(\{1,2,3,6,7,9\}\)
  • \(\emptyset\)

The correct choice is \(\{2,4,6,8,9,10\}\).

Final Answer

\[ \boxed{\{2,4,6,8,9,10\}} \]

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