To determine if [tex]\( R \subset A \)[/tex], we need to check if every element in set [tex]\( R \)[/tex] is also in set [tex]\( A \)[/tex].
First, let's examine the elements of each set:
- Set [tex]\( A \)[/tex] is defined as the set of all odd integers. Therefore, [tex]\( A = \{\ldots, -5, -3, -1, 1, 3, 5, 7, 9, \ldots\} \)[/tex].
- Set [tex]\( R \)[/tex] is given as [tex]\( R = \{3, 7, 11, 27\} \)[/tex].
Next, we analyze the elements of [tex]\( R \)[/tex]:
- The element [tex]\( 3 \)[/tex] is in set [tex]\( R \)[/tex]. Since 3 is an odd integer, it is also in set [tex]\( A \)[/tex].
- The element [tex]\( 7 \)[/tex] is in set [tex]\( R \)[/tex]. Since 7 is an odd integer, it is also in set [tex]\( A \)[/tex].
- The element [tex]\( 11 \)[/tex] is in set [tex]\( R \)[/tex]. Since 11 is an odd integer, it is also in set [tex]\( A \)[/tex].
- The element [tex]\( 27 \)[/tex] is in set [tex]\( R \)[/tex]. Since 27 is an odd integer, it is also in set [tex]\( A \)[/tex].
Since all elements in set [tex]\( R \)[/tex] (which are 3, 7, 11, and 27) are also elements of set [tex]\( A \)[/tex] (since they are all odd integers), we conclude that [tex]\( R \subset A \)[/tex].
Thus, the correct answer is:
Yes, because all the elements of set [tex]\( R \)[/tex] are in set [tex]\( A \)[/tex].
If we were to summarize the answer less formally, we'd say:
Yes, [tex]\( R \)[/tex] is a subset of [tex]\( A \)[/tex].
