To determine if [tex]\( R \subset A \)[/tex], we need to check if every element in set [tex]\( R \)[/tex] is also an element in set [tex]\( A \)[/tex].
Here are the sets given:
[tex]\[
U = \{ x \mid x \text{ is a real number} \}
\][/tex]
[tex]\[
A = \{ x \mid x \text{ is an odd integer} \}
\][/tex]
[tex]\[
R = \{ x \mid x = 3, 7, 11, 27 \}
\][/tex]
Let's examine the elements of set [tex]\( R \)[/tex]:
- The elements of [tex]\( R \)[/tex] are [tex]\( \{ 3, 7, 11, 27 \} \)[/tex].
Next, let's define set [tex]\( A \)[/tex]:
- Set [tex]\( A \)[/tex] contains all odd integers. So [tex]\( A \)[/tex] includes numbers like [tex]\(-1, 1, 3, 5, 7, 9, 11, \dots, \)[/tex].
Now, we check if each element of [tex]\( R \)[/tex] is in [tex]\( A \)[/tex]:
- [tex]\( 3 \)[/tex] is an odd integer and is in [tex]\( A \)[/tex].
- [tex]\( 7 \)[/tex] is an odd integer and is in [tex]\( A \)[/tex].
- [tex]\( 11 \)[/tex] is an odd integer and is in [tex]\( A \)[/tex].
- [tex]\( 27 \)[/tex] is an odd integer and is in [tex]\( A \)[/tex].
Since all the elements [tex]\( 3, 7, 11, 27 \)[/tex] in set [tex]\( R \)[/tex] are also in set [tex]\( A \)[/tex], we can conclude that [tex]\( R \subset A \)[/tex].
Therefore, the correct statement is:
[tex]\[ \text{Yes, because all the elements of set } R \text{ are in set } A. \][/tex]
