Answered

QUESTION 7

The outcomes of two events are:
[tex]\[
\begin{array}{c}
P = \{10, 12, 13, 14, 15, 16, 17, 18, 19, 20\} \text{ and } \\
Q = \{8, 9, 10, 11, 12, 13, 15\}.
\end{array}
\][/tex]

The intersection of [tex]\(P\)[/tex] and [tex]\(Q\)[/tex] is

A. [tex]\(\{8, 9, 11, 15\}\)[/tex]

B. [tex]\(\{12, 14, 16, 17, 18, 19, 20\}\)[/tex]

C. [tex]\(\{10, 12, 13\}\)[/tex]

D. [tex]\(\{10, 12, 13, 15\}\)[/tex]



Answer :

GinnyAnswer
To find the intersection of the given sets [tex]\( P \)[/tex] and [tex]\( Q \)[/tex], we need to determine all the elements that both sets share.

The set [tex]\( P \)[/tex] is:
[tex]\[ P = \{10, 12, 13, 14, 15, 16, 17, 18, 19, 20\} \][/tex]

The set [tex]\( Q \)[/tex] is:
[tex]\[ Q = \{8, 9, 10, 11, 12, 13, 15\} \][/tex]

Now, we will list the elements that are common to both sets [tex]\( P \)[/tex] and [tex]\( Q \)[/tex].

- [tex]\( 10 \)[/tex] is in both [tex]\( P \)[/tex] and [tex]\( Q \)[/tex].
- [tex]\( 12 \)[/tex] is in both [tex]\( P \)[/tex] and [tex]\( Q \)[/tex].
- [tex]\( 13 \)[/tex] is in both [tex]\( P \)[/tex] and [tex]\( Q \)[/tex].
- [tex]\( 15 \)[/tex] is in both [tex]\( P \)[/tex] and [tex]\( Q \)[/tex].

Thus, the intersection of [tex]\( P \)[/tex] and [tex]\( Q \)[/tex] is
[tex]\[ \{10, 12, 13, 15\} \][/tex]

So, the correct choice is:
(D.) [tex]\(\{10, 12, 13, 15\}\)[/tex]