Problem

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 $A^{\mathrm{c}}$ from the choices below.
$\{2,3,6,7,9,10\}$
$\{2,3,4,6,7,8\}$
$\{1,5,6,7,9,10\}$
$\{1,3,4,7,9,10\}$
$\{2,4,6,8,9,10\}$
$\emptyset$

Answer

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Answer

Final Answer: The complement of set A in the universal set U is $\boxed{\{2,4,6,8,9,10\}}$.

Steps

Step 1 :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 $A^{\mathrm{c}}$ from the choices below.

Step 2 :The question is asking for the complement of set A in the universal set U. The complement of a set A, denoted by A', is the set of all elements in the universal set that are not in A.

Step 3 :In this case, the universal set U is $\{1,2,3,...,10\}$ and set A is $\{1,3,5,7\}$. So, the complement of A would be all the numbers in U that are not in A.

Step 4 :U = $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$

Step 5 :A = $\{1, 3, 5, 7\}$

Step 6 :A_complement = $\{2, 4, 6, 8, 9, 10\}$

Step 7 :Final Answer: The complement of set A in the universal set U is $\boxed{\{2,4,6,8,9,10\}}$.

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