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Let $P = \{-10, -9, -8\}$ and $Q = \{-9, -8, -7, -6, -5\}$ . What is $P \cap Q$ ? $\newline$ Choices: $\newline$ (A) $\{-10, -9, -8, -5\}$ $\newline$ (B) $\{-8\}$ $\newline$ (C) $\{-9, -8\}$ $\newline$ (D) $\{-10, -9, -8, -7, -6, -5\}$

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Full solution

Q. Let

P = \{-10, -9, -8\}

and

Q = \{-9, -8, -7, -6, -5\}

. What is

P \cap Q

?

\newline

Choices:

\newline

(A)

\{-10, -9, -8, -5\}

\newline

(B)

\{-8\}

\newline

(C)

\{-9, -8\}

\newline

(D)

\{-10, -9, -8, -7, -6, -5\}

Identify Common Elements: To find the intersection of two sets, we need to identify the elements that are common to both sets.
Given Sets: Set $P$ contains the elements $\{-10, -9, -8\}$ . $\newline$ Set $Q$ contains the elements $\{-9, -8, -7, -6, -5\}$ .
Comparison of Elements: By comparing the elements of $P$ and $Q$ , we can see that the common elements are $-9$ and $-8$ .
Intersection of Sets: Therefore, the intersection of sets $P$ and $Q$ , denoted by $P \cap Q$ , is the set containing the elements $\{-9, -8\}$ .
Correct Answer: Looking at the given choices, the correct answer is (C) $\{-9, -8\}$ .

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