Part-I: Write true if the statement is true or false if the statement is false. (1pt each) 1. If \( A=\{0,1,2\} \) and \( B=\{x \in R \mid 0 \leq x \leq 2\} \), then \( A=B \). 2. \( \{\emptyset\} \) is both the element and the subset of \( \{\emptyset,\{\emptyset\}\} \). 3. If the truth value of \( p \Rightarrow q \) is \( F \), then the truth values of \( (\neg p \wedge q) \Leftrightarrow(p \vee q) \) is false. 4. If \( A=\{x \in Z \mid x \) is divisible by 2\( \} \) and \( B=\{y \in Z \mid y \) is divisible by 3\( \} \), then \( A \cap B \) is \( \emptyset \).

Part-III: Choose the best answer from given choice (Ipt eacil 11. Let \( B=\{\emptyset,\{\emptyset,\{\emptyset\}\}\} \). Then the number of proper subset is \( \begin{array}{llll}\text { A. } 8 & \text { B. } 7 & \text { C. } 3 & \text { D. } 4\end{array} \)

Part-III: Choose the best answer from given choice (1pt eacil) 11. Let \( \mathrm{B}=\{\emptyset,\{\emptyset,\{\emptyset\}\}\} \). Then the number of proper subset is \( \begin{array}{llll}\text { A. } 8 & \text { B. } 7 & \text { C. } 3 & \text { D. } 4\end{array} \)

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(c) Let \( B=\left(\begin{array}{ll}1 & 3 \\ 5 & 3\end{array}\right) \). Find a nonzero column vector \( \mu=\binom{x}{y} \) such that \( B \mu=6 \mu \).

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