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Let $G = \{-9, 9\}$ and $H = \{-10, -9\}$ . What is $G \cap H$ ? $\newline$ Choices: $\newline$ (A) $\{-10\}$ $\newline$ (B) $\{-9\}$ $\newline$ (C) $\{-10, -9, 9\}$ $\newline$ (D) $\{-10, 9\}$

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Full solution

Q. Let

G = \{-9, 9\}

and

H = \{-10, -9\}

. What is

G \cap H

?

\newline

Choices:

\newline

(A)

\{-10\}

\newline

(B)

\{-9\}

\newline

(C)

\{-10, -9, 9\}

\newline

(D)

\{-10, 9\}

Define Intersection of Sets: The question prompt asks us to find the intersection of two sets $G$ and $H$ , which is denoted by $G \cap H$ . The intersection of two sets is the set of elements that are common to both sets.
List Elements of Sets: To find $G \cap H$ , we list the elements of each set and identify any elements that appear in both sets. The set $G$ is given as \{ $-9$ , $9$ \}, and the set $H$ is given as \{ $-10$ , $-9$ \}.
Identify Common Elements: Comparing the elements of $G$ and $H$ , we see that the element $-9$ is present in both sets. The element $9$ is only in set $G$ , and the element $-10$ is only in set $H$ .
Find Intersection of G and H: Therefore, the intersection of sets $G$ and $H$ , $G \cap H$ , is the set containing only the element that is in both $G$ and $H$ , which is $\{-9\}$ .

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