Certainly! Let's solve the problem step-by-step.
Given, [tex]\( A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \)[/tex].
First, identify the subset of odd numbers within [tex]\( A \)[/tex]:
- The elements of [tex]\( A \)[/tex] that are odd are: [tex]\( 1, 3, 5, 7, 9 \)[/tex].
So, the subset of odd numbers is [tex]\( \{1, 3, 5, 7, 9\} \)[/tex].
Next, identify the subset of multiples of 3 within [tex]\( A \)[/tex]:
- The elements of [tex]\( A \)[/tex] that are multiples of 3 are: [tex]\( 3, 6, 9 \)[/tex].
So, the subset of multiples of 3 is [tex]\( \{3, 6, 9\} \)[/tex].
Finally, find the intersection of these two subsets:
- The elements that are both odd and multiples of 3 are: [tex]\( 3 \)[/tex] and [tex]\( 9 \)[/tex].
Therefore, the elements that are in both the subset of odd numbers and the subset of multiples of 3 are [tex]\( 3 \)[/tex] and [tex]\( 9 \)[/tex]. So, the answer is [tex]\( \{3, 9\} \)[/tex].
To summarize:
- The odd numbers in set [tex]\( A \)[/tex] are [tex]\( \{1, 3, 5, 7, 9\} \)[/tex].
- The multiples of 3 in set [tex]\( A \)[/tex] are [tex]\( \{3, 6, 9\} \)[/tex].
- The numbers that are in both subsets are [tex]\( 3 \)[/tex] and [tex]\( 9 \)[/tex].
