Question
\( B=\{x \mid 17 \leq x \leq 29 \) and \( x \) is an even number \( \} \)
Ask by Hills Hobbs. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The set \( B \) includes the even numbers from 18 to 28: \( \{18, 20, 22, 24, 26, 28\} \).
Solution
1. The condition is \( 17 \leq x \leq 29 \) and \( x \) is an even number.
2. The smallest even number greater than or equal to 17 is \( 18 \).
3. The even numbers within the interval are obtained by adding \( 2 \) repeatedly:
- \( 18 \)
- \( 18 + 2 = 20 \)
- \( 20 + 2 = 22 \)
- \( 22 + 2 = 24 \)
- \( 24 + 2 = 26 \)
- \( 26 + 2 = 28 \)
4. The next even number, \( 30 \), exceeds \( 29 \), so it is not included.
Thus, the set is
\[
B = \{18, 20, 22, 24, 26, 28\}.
\]
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Simplify this solution Beyond the Answer
Did you know that the set \( B \) includes all the even numbers between 17 and 29? So, if you list them out, you get \( B = \{18, 20, 22, 24, 26, 28\} \). It's fascinating how sets can help us organize numbers based on certain conditions! This kind of set notation comes in handy in various fields! In programming, for example, you might use similar logic to filter even numbers from a list. This can simplify code and improve efficiency when dealing with large datasets, making it easier to analyze or manipulate the data.
