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Let $R = \{7\}$ and $S = \{2, 3, 4, 5, 6\}$ . What is $R \cup S$ ? $\newline$ Choices: $\newline$ (A) $\{2, 3, 5, 6\}$ $\newline$ (B) $\{2, 7\}$ $\newline$ (C) $\emptyset$ $\newline$ (D) $\{2, 3, 4, 5, 6, 7\}$

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Unions and intersections of sets

Full solution

Q. Let

R = \{7\}

and

S = \{2, 3, 4, 5, 6\}

. What is

R \cup S

?

\newline

Choices:

\newline

(A)

\{2, 3, 5, 6\}

\newline

(B)

\{2, 7\}

\newline

(C)

\emptyset

\newline

(D)

\{2, 3, 4, 5, 6, 7\}

Concept of union of sets: Understand the concept of union of sets. $\newline$ The union of two sets $R$ and $S$ , denoted by $R \cup S$ , is the set of all elements that are in $R$ , or in $S$ , or in both. It includes every distinct element from both sets.
Elements of set R: Identify the elements of set R. $\newline$ Set R is given as $R = \{7\}$ . It contains only one element, which is $7$ .
Elements of set S: Identify the elements of set S. $\newline$ Set S is given as $S = \{2, 3, 4, 5, 6\}$ . It contains the elements $2$ , $3$ , $4$ , $5$ , and $6$ .
Combine elements for union: Combine the elements of sets $R$ and $S$ to form the union. $\newline$ Since $R$ contains the element $7$ and $S$ contains the elements $2$ , $3$ , $4$ , $5$ , and $6$ , the union of $R$ and $S$ will contain all these elements without repetition. $\newline$ $S$ $2$ .

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