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Let $S = \{3\}$ and $T = \{2, 8, 9, 14\}$ . What is $S \cup T$ ? $\newline$ Choices: $\newline$ (A) $\{3, 8, 9, 14\}$ $\newline$ (B) $\{2, 3, 9\}$ $\newline$ (C) $\{2, 3, 8, 9, 14\}$ $\newline$ (D) $\emptyset$

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Unions and intersections of sets

Full solution

Q. Let

S = \{3\}

and

T = \{2, 8, 9, 14\}

. What is

S \cup T

?

\newline

Choices:

\newline

(A)

\{3, 8, 9, 14\}

\newline

(B)

\{2, 3, 9\}

\newline

(C)

\{2, 3, 8, 9, 14\}

\newline

(D)

\emptyset

Understand union concept: Understand the concept of union of sets. $\newline$ The union of two sets $S$ and $T$ , denoted by $S \cup T$ , is the set of all elements that are in $S$ , or in $T$ , or in both. This means we combine the elements of both sets without repeating any elements.
Identify set elements: Identify the elements of set $S$ and set $T$ . We have $S = \{3\}$ and $T = \{2, 8, 9, 14\}$ . These are the elements we will combine to form the union.
Combine elements for union: Combine the elements of $S$ and $T$ to form the union. $\newline$ Since $S$ has only one element, which is $3$ , and $T$ has four elements, which are $2$ , $8$ , $9$ , and $14$ , the union will include all these elements without repetition. Therefore, $S \cup T = \{2, 3, 8, 9, 14\}$ .

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