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Math 170(J. Wu) Answers to Homeworks
Homework 2:

page 48

10.
\begin{diagram} 1878=2\times 939=2\times 3\times 313\\ \end{diagram}
Thus
\begin{diagram} P(1878)=S(1878)-1878=(1+2)\times (1+3)\times (1+313)-1878\\ =3\times 4\times 314-1878=1890.\end{diagram}

11. (see the book).

12.
\begin{diagram} 4173=3\times 1391=3\times 13\times 107.\\ \end{diagram}
Thus
\begin{diagram} P(4173)=S(4173)-4173=(1+3)\times (1+13)\times (1+107)-4173\\ =4\times 14\times 108-4173\\ =6048-4173=1875.\\ \end{diagram}

13. (see the book)

15.(see the book)

Page 54

3. (see the book)

Page 136

24.

\begin{displaymath} B\times C=\{(3,5),(3,6),(4,5),(4,6),(5,5),(5,6),(6,5),(6,6)\}.\end{displaymath}

25. (see the book)

26.

\begin{displaymath} A'\cup B'=\{0,4,5,6,7,8,9\}\cup \{0,1,2,7,8,9\}=\{0,1,2,4,5,6,7,8,9\}.\end{displaymath}

27.

\begin{displaymath} (A\cap B)'=A'\cup B'.\end{displaymath}

28.

\begin{displaymath} A'\cap B'=\{0,4,5,6,7,8,9\}\cap \{0,1,2,7,8,9\}=\{0,7,8,9\}.\end{displaymath}


 
Jie Wu
11/13/1997