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

\newline

(B)

\{7, 8\}

\newline

(C)

\{-10, 1\}

\newline

(D)

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

Concept of Union: Understand the concept of union of sets. The union of two sets $P$ and $Q$ , denoted by $P \cup Q$ , is the set of elements which are in $P$ , in $Q$ , or in both $P$ and $Q$ .
Elements of Set P: List the elements of set $P$ . $P = \{1, 7, 8\}$
Elements of Set Q: List the elements of set $Q$ . $\newline$ $Q = \{-10, 7, 8\}$
Combine Elements: Combine the elements of $P$ and $Q$ without repeating any elements 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 them only once.

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