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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) $\emptyset$ $\newline$ (C) $\{2, 3, 8, 9, 14\}$ $\newline$ (D) $\{2, 3, 9\}$

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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)

\emptyset

\newline

(C)

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

\newline

(D)

\{2, 3, 9\}

Understand concept of union: 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. It includes all the unique elements from both sets.
Identify elements of sets: Identify the elements of set $S$ and set $T$ . We have $S = \{3\}$ and $T = \{2, 8, 9, 14\}$ .
Combine elements to form union: Combine the elements of $S$ and $T$ to form the union. $\newline$ Since the union includes all unique elements from both sets, we combine them while avoiding repetition of elements. $\newline$ $S \cup T = \{3\} \cup \{2, 8, 9, 14\} = \{2, 3, 8, 9, 14\}$ .

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