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Let $D = \{0, 1, 5, 7, 8\}$ and $E = \{1, 8\}$ . What is $D \cup E$ ? $\newline$ Choices: $\newline$ (A) $\{0, 5, 7\}$ $\newline$ (B) $\{1\}$ $\newline$ (C) $\{1, 8\}$ $\newline$ (D) $\{0, 1, 5, 7, 8\}$

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Unions and intersections of sets

Full solution

Q. Let

D = \{0, 1, 5, 7, 8\}

and

E = \{1, 8\}

. What is

D \cup E

?

\newline

Choices:

\newline

(A)

\{0, 5, 7\}

\newline

(B)

\{1\}

\newline

(C)

\{1, 8\}

\newline

(D)

\{0, 1, 5, 7, 8\}

Understand Union of Sets: Understand the concept of union of sets. $\newline$ The union of two sets $D$ and $E$ , denoted by $D \cup E$ , is the set of all elements that are in $D$ , or in $E$ , or in both. It includes every distinct element from both sets.
Identify Elements in Sets: Identify the elements in set $D$ and set $E$ . We have: $D = \{0, 1, 5, 7, 8\}$ $E = \{1, 8\}$
Combine Elements for Union: Combine the elements of set $D$ and set $E$ to form the union. $\newline$ Since the union includes all unique elements from both sets, we combine them while removing duplicates: $\newline$ $D \cup E = \{0, 1, 5, 7, 8\}$ $\newline$ Note that $1$ and $8$ are in both sets, but we only list them once in the union.

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