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Let $G = \{-3, -1, 0, 5\}$ and $H = \{0, 3, 5\}$ . What is $G \cap H$ ? $\newline$ Choices: $\newline$ (A) $\{0, 5\}$ $\newline$ (B) $\{-3, -1, 0, 3, 5\}$ $\newline$ (C) $\{5\}$ $\newline$ (D) $\{0, 3, 5\}$

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Unions and intersections of sets

Full solution

Q. Let

G = \{-3, -1, 0, 5\}

and

H = \{0, 3, 5\}

. What is

G \cap H

?

\newline

Choices:

\newline

(A)

\{0, 5\}

\newline

(B)

\{-3, -1, 0, 3, 5\}

\newline

(C)

\{5\}

\newline

(D)

\{0, 3, 5\}

Understand Intersection of Sets: Understand what the intersection of two sets means. $\newline$ The intersection of two sets $G$ and $H$ , denoted by $G \cap H$ , includes all the elements that are common to both sets $G$ and $H$ .
Identify Common Elements: Identify the common elements in sets $G$ and $H$ . We have: $G = \{-3, -1, 0, 5\}$ $H = \{0, 3, 5\}$ The common elements in both sets are $0$ and $5$ .
Write Intersection: Write down the intersection of sets $G$ and $H$ . $G \cap H = \{0, 5\}$

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