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Let $M = \{2, 4, 6, 8, 10\}$ and $N = \{2, 6, 8, 10, 14, 16\}$ . What is $M \cap N$ ? $\newline$ Choices: $\newline$ (A) $\{2, 6, 8, 10, 14, 16\}$ $\newline$ (B) $\{6, 8, 10\}$ $\newline$ (C) $\{2, 4, 6, 8, 10, 14, 16\}$ $\newline$ (D) $\{2, 6, 8, 10\}$

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Unions and intersections of sets

Full solution

Q. Let

M = \{2, 4, 6, 8, 10\}

and

N = \{2, 6, 8, 10, 14, 16\}

. What is

M \cap N

?

\newline

Choices:

\newline

(A)

\{2, 6, 8, 10, 14, 16\}

\newline

(B)

\{6, 8, 10\}

\newline

(C)

\{2, 4, 6, 8, 10, 14, 16\}

\newline

(D)

\{2, 6, 8, 10\}

Understand Intersection Definition: Understand what $M \cap N$ represents. $\newline$ The intersection of two sets, denoted by $M \cap N$ , includes all the elements that are common to both sets $M$ and $N$ .
List Elements of Sets: List the elements of set $M$ and set $N$ . We have: $M = \{2, 4, 6, 8, 10\}$ $N = \{2, 6, 8, 10, 14, 16\}$
Identify Common Elements: Identify the common elements in sets $M$ and $N$ . The common elements that appear in both sets are $2$ , $6$ , $8$ , and $10$ .
Write Intersection Result: Write down the intersection of $M$ and $N$ . $\newline$ $M \cap N = \{2, 6, 8, 10\}$

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