(Solved): a) Among Boolean functions of degree 3 , the total number of bijcctive functions is b) Assume that ...

a) Among Boolean functions of degree 3 , the total number of bijcctive functions is b) Assume that there are 5 Boolean variables: \( x_{1}, x_{2}, x_{3}, x_{4} \), and \( x_{5} \). Write down the minterm \( \quad \) that equals 1 if \( x_{1}=x_{2}=x_{3}=1 \) and \( x_{4}=x_{5}=0 \), and equals 0 otherwise. C) Let \( R_{1}=\phi \) be an empty binary relation on the sct \( A=\{a, b, c\} \). Then the transitive closure of \( R_{1} \) is. d) In the poset \( (\{1,2,4,5,10,12,20,25\}, \mid) \), where \( \mid \) denotes divisibility, the minimal elements are e) Let \( A=\{a, b, c, d, e, f\} \), and the relation \( R_{1} \) on \( A \) be \( \{\langle a, e\rangle,\langle b, c\rangle,\langle d, f\rangle\} \). The equivalence relation \( R_{2} \) on \( A \) satisfies \( R_{1} \subseteq R_{2} \). Then how many \( R_{2} \) can be defined at most on \( A \) ? 7) Write down all generators of \( \left\langle\mathbf{Z}_{6}, \oplus>\right. \), , where \( \oplus \) is addition modula 6 . 8) In field \( \mathbf{Z}_{7} \), with respect to addition and multiplication modula 7 , the solution to the equation \( 3 x=5 \) is