To determine which description could apply to the universal set [tex]\( U \)[/tex] that contains subset [tex]\( S \)[/tex], consider the elements within [tex]\( S \)[/tex]:
[tex]\[ S = \{x, y, 4, 9, ?\} \][/tex]
Let's analyze each element in [tex]\( S \)[/tex]:
1. [tex]\( x \)[/tex] - this is a letter.
2. [tex]\( y \)[/tex] - this is a letter.
3. [tex]\( 4 \)[/tex] - this is a number.
4. [tex]\( 9 \)[/tex] - this is a number.
5. [tex]\( ? \)[/tex] - this is a punctuation mark.
Given the diverse nature of these elements, [tex]\( U \)[/tex] must be a set that can include letters, numbers, and punctuation marks. Let's evaluate each option:
1. U = {keys on a keyboard}: This option is plausible because keyboards have letters, numbers, and punctuation marks.
2. U = {letters}: This option is not plausible because [tex]\( S \)[/tex] includes numbers and a punctuation mark, which are not letters.
3. U = {numbers}: This option is not plausible because [tex]\( S \)[/tex] includes letters and a punctuation mark, not just numbers.
4. U = {punctuation marks}: This option is not plausible because [tex]\( S \)[/tex] includes letters and numbers, not just punctuation marks.
Therefore, the option that could reasonably describe the universal set [tex]\( U \)[/tex] is:
U = {keys on a keyboard}.
