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Let $P = \{3, 5, 7, 9, 11\}$ and $Q = \{2, 4, 6, 8\}$ . What is $P \cap Q$ ? $\newline$ Choices: $\newline$ (A) $\{2, 3, 4, 6, 7, 8, 9, 11\}$ $\newline$ (B) $\{2, 3, 4, 5, 6, 7, 8\}$ $\newline$ (C) $\{2, 3, 4, 5, 6, 7, 8, 9, 11\}$ $\newline$ (D) $\emptyset$

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Triangle inequality

Full solution

Q. Let

P = \{3, 5, 7, 9, 11\}

and

Q = \{2, 4, 6, 8\}

. What is

P \cap Q

?

\newline

Choices:

\newline

(A)

\{2, 3, 4, 6, 7, 8, 9, 11\}

\newline

(B)

\{2, 3, 4, 5, 6, 7, 8\}

\newline

(C)

\{2, 3, 4, 5, 6, 7, 8, 9, 11\}

\newline

(D)

\emptyset

Understand intersection concept: Understand the concept of intersection. The intersection of two sets, denoted by $P \cap Q$ , is the set containing all elements that are both in $P$ and in $Q$ .
Identify elements in set P: Identify the elements in set P. $\newline$ Set $P = \{3, 5, 7, 9, 11\}$
Identify elements in set Q: Identify the elements in set Q. Set $Q = \{2, 4, 6, 8\}$
Find common elements: Find the common elements between set $P$ and set $Q$ . By comparing the elements of $P$ and $Q$ , we see that there are no elements that are present in both sets.
Conclude intersection of $P$ and $Q$ : Conclude the intersection of $P$ and $Q$ . Since there are no common elements, the intersection of $P$ and $Q$ is the empty set, denoted by $\emptyset$ .

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