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Let $P = \{1, 7, 8\}$ and $Q = \{-10, 7, 8\}$ . What is $P \cup Q$ ? $\newline$ Choices: $\newline$ (A) $\{7, 8\}$ $\newline$ (B) $\{-10, 1\}$ $\newline$ (C) $\{7\}$ $\newline$ (D) $\{-10, 1, 7, 8\}$

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Transformations of linear functions

Full solution

Q. Let

P = \{1, 7, 8\}

and

Q = \{-10, 7, 8\}

. What is

P \cup Q

?

\newline

Choices:

\newline

(A)

\{7, 8\}

\newline

(B)

\{-10, 1\}

\newline

(C)

\{7\}

\newline

(D)

\{-10, 1, 7, 8\}

Define Union of Sets: Identify the definition of the union of two sets. $\newline$ The union of two sets $P$ and $Q$ , denoted by $P \cup Q$ , is the set of all elements that are in $P$ , in $Q$ , or in both $P$ and $Q$ .
List Elements in Set P: List all the elements in set $P$ . $P = \{1, 7, 8\}$
List Elements in Set Q: List all the elements in set $Q$ . $\newline$ $Q = \{-10, 7, 8\}$
Combine Unique Elements: Combine all unique elements from sets $P$ and $Q$ to form the union. $P \cup Q = \{1, 7, 8, -10\}$ Note that $7$ and $8$ are in both $P$ and $Q$ , but we list each element only once in the union.
Match with Choices: Match the resulting set with the given choices. $\newline$ The union set $P \cup Q = \{1, 7, 8, -10\}$ matches with choice (D)\{ $-10$ , $1$ , $7$ , $8$ \}.

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