Precálculo Sec. 1.1

Un poquito de lógica y de conjuntos

Si \(\mathit{U} = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}\), \(A = \{x \in \mathit{U} / x \mbox{ es par}\}\), \(B = \{x / x \mbox{ es primo}\}\) y \(D = \{ x \in \mathit{U} / x \mbox{ no es divisor de 9} \}\), hallar:
1. \[ \complement (A \cup B) \]
2. \[ A - \complement D \]
3. \[ B - \complement D \]
4. \[ (A-B) \cup (B-A) \]
Si \(\mathit{U} = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\} \), hallar conjuntos \(A\) y \(B\) tales que:
1. \[ A - B = \{7, 9\} \]
2. \[ \complement A \cap \complement B = \{ 6 \} \]
3. \[ A \cap B = \{ 0, 5, 8 \} \]
Si \(\mathit{U} = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}\), hallar conjuntos \(A\) y \(B\) tales que:
1. \[ (A - B) \cup (B - A) = \{0, 1, 5, 8\} \]
  
  \[ \begin{aligned} &(A - B) \cup (B - A) \\[1em] &\hspace{5em}= \{0, 1, 5, 8\} \end{aligned} \]
2. \[ \complement A \cup \complement B = \{ 0, 1, 2, 5, 6, 7, 8 \} \]
3. \[ A \cap \complement B = \{ 0, 8\} \]
Hallar los conjuntos \(A\), \(B\), \(C\) y \(U\), el conjunto universal, sabiendo que:
1. \[ \complement A = \{1, 4, 7, 8, 9\} \]
2. \[ \complement B = \{2, 4, 5, 7\} \]
3. \[ \complement C = \{2, 4, 7, 8\} \]
4. \[ A \cap B \cap C = \{0, 3, 6\} \]

1. \(\{ 1, 9\}\)
2. \(A=\{ 2,4,6,8 \}\)
3. \(\{ 2,5,7 \}\)
4. \(\{ 3,4,5,6,7 \}\)
\[ A = \{ 0,5,7,8,9 \}, \quad B = \{ 0,1,2,3,4,5,8 \} \]

\[ \begin{aligned} &A = \{ 0,5,7,8,9 \}, \\[1em] &B = \{ 0,1,2,3,4,5,8 \} \end{aligned} \]
\[ A = \{ 0,3,4,8,9 \}, \quad B = \{ 1,3,5,6,9 \} \]

\[ \begin{aligned} &A = \{ 0,3,4,8,9 \}, \\[1em] &B = \{ 1,3,5,6,9 \} \end{aligned} \]
\[ A = \{ 0, 2 , 3 , 6 \} , \quad B = \{ 0, 1, 2, 6, 8, 9 \}, \quad C = \{ 0, 1, 3, 5, 6, 9 \}, \quad U = \{ 0, 1, 3, 4, 5, 6, 8, 9 \} \]

\[ \begin{aligned} &A = \{ 0, 2 , 3 , 6 \} , \\[1em] &B = \{ 0, 1, 2, 6, 8, 9 \}, \\[1em] &C = \{ 0, 1, 3, 5, 6, 9 \}, \\[1em] &U = \{ 0, 1, 3, 4, 5, 6, 8, 9 \} \end{aligned} \]