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Let $D = \{1, 4\}$ and $E = \{0, 1, 2, 3, 4\}$ . What is $D \cap E$ ? $\newline$ Choices: $\newline$ (A) $\{4\}$ $\newline$ (B) $\{0, 1, 2, 3, 4\}$ $\newline$ (C) $\{1, 4\}$ $\newline$ (D) $\{1, 2, 3, 4\}$

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Full solution

Q. Let

D = \{1, 4\}

and

E = \{0, 1, 2, 3, 4\}

. What is

D \cap E

?

\newline

Choices:

\newline

(A)

\{4\}

\newline

(B)

\{0, 1, 2, 3, 4\}

\newline

(C)

\{1, 4\}

\newline

(D)

\{1, 2, 3, 4\}

Determine Set D: Determine the elements of set D. $\newline$ Set D = ${1, 4}$ .
Determine Set E: Determine the elements of set E. $\newline$ Set E = ${0, 1, 2, 3, 4}$ .
Calculate Intersection: Calculate the intersection of sets $D$ and $E$ , which is the set of elements that are common to both $D$ and $E$ . $D \cap E = \{1, 4\}$ .
Match with Choices: Match the result of the intersection with the given choices. $\newline$ The intersection of $D$ and $E$ is \{ $1$ , $4$ \}, which matches choice $(C)$ .

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