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Let $D = \{5\}$ and $E = \{5, 15, 25, 35\}$ . What is $D \cup E$ ? $\newline$ Choices: $\newline$ (A) $\{5, 15, 25, 35\}$ $\newline$ (B) $\{15, 25, 35\}$ $\newline$ (C) $\{25\}$ $\newline$ (D) $\emptyset$

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Full solution

Q. Let

D = \{5\}

and

E = \{5, 15, 25, 35\}

. What is

D \cup E

?

\newline

Choices:

\newline

(A)

\{5, 15, 25, 35\}

\newline

(B)

\{15, 25, 35\}

\newline

(C)

\{25\}

\newline

(D)

\emptyset

Initialize Sets: $D = \{5\}$ and $E = \{5, 15, 25, 35\}$ . To find the union of two sets, we combine all the unique elements from both sets.
Find Union: The union of $D$ and $E$ , denoted by $D \cup E$ , will include all the elements from $D$ and all the elements from $E$ without repeating any elements.
Combine Unique Elements: Since $5$ is present in both $D$ and $E$ , it will only be listed once in the union. The rest of the elements from $E$ will be included as they are not present in $D$ .
Final Union: Therefore, $D \cup E = \{5, 15, 25, 35\}$ .
Correct Answer: Comparing the result with the given choices, we find that the correct answer is (A) ${5, 15, 25, 35}$ .

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