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Let $G = \{2, 4, 6, 8, 10\}$ and $H = \{10\}$ . What is $G \cup H$ ? $\newline$ Choices: $\newline$ (A) $\{10\}$ $\newline$ (B) $\{2, 4\}$ $\newline$ (C) $\{2, 4, 6, 8\}$ $\newline$ (D) $\{2, 4, 6, 8, 10\}$

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Write variable expressions for arithmetic sequences

Full solution

Q. Let

G = \{2, 4, 6, 8, 10\}

and

H = \{10\}

. What is

G \cup H

?

\newline

Choices:

\newline

(A)

\{10\}

\newline

(B)

\{2, 4\}

\newline

(C)

\{2, 4, 6, 8\}

\newline

(D)

\{2, 4, 6, 8, 10\}

Explanation: To find the union of two sets, we combine all the unique elements from both sets. The union is represented by the symbol $\cup$ . $\newline$ $G = \{2, 4, 6, 8, 10\}$ $\newline$ $H = \{10\}$ $\newline$ We need to list all the elements from both sets without repeating any elements.
Combining Sets: Since $10$ is already in set $G$ , we do not need to list it again. The union of $G$ and $H$ will include all the elements from $G$ and any elements from $H$ that are not already in $G$ . $\newline$ $G \cup H = \{2, 4, 6, 8, 10\}$
Comparing Results: Now we compare the result with the given choices to find the correct answer. $\newline$ (A) ${10}$ - Incorrect, as it does not include all elements from $G$ . $\newline$ (B) ${2, 4}$ - Incorrect, as it is missing elements from $G$ . $\newline$ (C) ${2, 4, 6, 8}$ - Incorrect, as it is missing the element $10$ from $G$ . $\newline$ (D) ${2, 4, 6, 8, 10}$ - Correct, as it includes all unique elements from both sets $G$ and $H$ .

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