Pregunta
Question 5 1 pts Given \( A=\{a, b, c\}, B=\{c, d, f\}, C=\{c, d, f, g\} \) Is \( B \subset C \) ? Yes No
Ask by Garza Gray. in the United States
Mar 17,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( B \) is a subset of \( C \), so the answer is Yes.
Solución
1. Given the sets, we have:
- \( B = \{c, d, f\} \)
- \( C = \{c, d, f, g\} \)
2. To determine whether \( B \subset C \), we check if every element of \( B \) is also an element of \( C \):
- For \( c \): Since \( c \in C \), the condition is satisfied.
- For \( d \): Since \( d \in C \), the condition is satisfied.
- For \( f \): Since \( f \in C \), the condition is satisfied.
3. Since all elements of \( B \) are found in \( C \), we conclude that:
\[
B \subset C
\]
4. Therefore, the answer is: Yes.
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Simplifique esta solución Bonus Knowledge
Yes, \( B \) is indeed a subset of \( C \). In set theory, a set \( B \) is considered a subset of another set \( C \) if every element of \( B \) is also an element of \( C \). Since both \( c \) and \( d \) from set \( B \) are present in set \( C \), we can confidently say that \( B \subset C \) holds true! Additionally, this relationship highlights the beauty of set inclusion in mathematics. It shows how elements can connect different sets and helps in the analysis of relationships between data. Understanding subsets is crucial, especially in fields like computer science and data analysis, where organizing and categorizing information is essential.
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