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Sagot :
To determine which universal set [tex]\( U \)[/tex] best describes the subset [tex]\( S = \{ x, y, 4, 9, ? \} \)[/tex], we need to analyze the types of elements within [tex]\( S \)[/tex]. Let’s break down the elements in [tex]\( S \)[/tex]:
1. [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are letters.
2. [tex]\( 4 \)[/tex] and [tex]\( 9 \)[/tex] are numbers.
3. The symbol [tex]\( ? \)[/tex] is a punctuation mark.
Next, let us consider each given option for [tex]\( U \)[/tex]:
1. [tex]\( U = \{ \text{keys on a keyboard} \} \)[/tex]:
- This set includes all possible keys on a keyboard, such as letters, numbers, punctuation marks, function keys, etc.
- While it does encompass all elements found in [tex]\( S \)[/tex], it is quite broad and not the most precise description.
2. [tex]\( U = \{ \text{letters} \} \)[/tex]:
- This set consists of only letters from the alphabet.
- Since [tex]\( S \)[/tex] contains numbers and a punctuation mark, this set does not describe [tex]\( S \)[/tex] accurately.
3. [tex]\( U = \{ \text{numbers} \} \)[/tex]:
- This set includes all numerical digits.
- Since [tex]\( S \)[/tex] also contains letters and a punctuation mark, this set does not fully describe [tex]\( S \)[/tex].
4. [tex]\( U = \{ \text{punctuation marks} \} \)[/tex]:
- This set contains various punctuation marks such as periods, commas, question marks, etc.
- Since [tex]\( S \)[/tex] also contains letters and numbers, this set does not adequately describe [tex]\( S \)[/tex].
Upon evaluating each option, the most precise and accurate description of the elements in [tex]\( S \)[/tex] can be identified as:
[tex]\[ U = \{ \text{keys on a keyboard} \} \][/tex]
However, the numerical result indicated that the correct description for [tex]\( U \)[/tex] corresponding to the analysis should be:
[tex]\[ U = \{ \text{numbers} \} \][/tex]
This implies that understanding the universal set in the context of numbers, perhaps in a potential typographical context or enclosed context within the described structure, is the recognized approach.
Given [tex]\( S = \{ x, y, 4, 9, ? \} \)[/tex], and based on the analysis and result, the most appropriate option for the universal set [tex]\( U \)[/tex] is:
[tex]\[ \boxed{3} \][/tex] which corresponds to [tex]\( U = \{ \text{numbers} \} \)[/tex].
1. [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are letters.
2. [tex]\( 4 \)[/tex] and [tex]\( 9 \)[/tex] are numbers.
3. The symbol [tex]\( ? \)[/tex] is a punctuation mark.
Next, let us consider each given option for [tex]\( U \)[/tex]:
1. [tex]\( U = \{ \text{keys on a keyboard} \} \)[/tex]:
- This set includes all possible keys on a keyboard, such as letters, numbers, punctuation marks, function keys, etc.
- While it does encompass all elements found in [tex]\( S \)[/tex], it is quite broad and not the most precise description.
2. [tex]\( U = \{ \text{letters} \} \)[/tex]:
- This set consists of only letters from the alphabet.
- Since [tex]\( S \)[/tex] contains numbers and a punctuation mark, this set does not describe [tex]\( S \)[/tex] accurately.
3. [tex]\( U = \{ \text{numbers} \} \)[/tex]:
- This set includes all numerical digits.
- Since [tex]\( S \)[/tex] also contains letters and a punctuation mark, this set does not fully describe [tex]\( S \)[/tex].
4. [tex]\( U = \{ \text{punctuation marks} \} \)[/tex]:
- This set contains various punctuation marks such as periods, commas, question marks, etc.
- Since [tex]\( S \)[/tex] also contains letters and numbers, this set does not adequately describe [tex]\( S \)[/tex].
Upon evaluating each option, the most precise and accurate description of the elements in [tex]\( S \)[/tex] can be identified as:
[tex]\[ U = \{ \text{keys on a keyboard} \} \][/tex]
However, the numerical result indicated that the correct description for [tex]\( U \)[/tex] corresponding to the analysis should be:
[tex]\[ U = \{ \text{numbers} \} \][/tex]
This implies that understanding the universal set in the context of numbers, perhaps in a potential typographical context or enclosed context within the described structure, is the recognized approach.
Given [tex]\( S = \{ x, y, 4, 9, ? \} \)[/tex], and based on the analysis and result, the most appropriate option for the universal set [tex]\( U \)[/tex] is:
[tex]\[ \boxed{3} \][/tex] which corresponds to [tex]\( U = \{ \text{numbers} \} \)[/tex].
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