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- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- -z\in \mathbb{C} \mbox{ such that}\; z+\left( -z\right) =0 \\ \mbox{In fact if } z=a+bi, \mbox{ then } -... ber\] - Associative Law for Addition \[\left( z+w\right) +v= z +\left( w+v\right)\nonumber \] </panel> <panel> **Question 2** Verify the multiplication proper... $\quad (2,6)\div (3,7)=\dfrac{(2,6)}{\left( 3,7 \right)}$ $=\dfrac{2+6i}{3+7i}=\dfrac{2+6i}{3+7i}\times
- Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
- y} \] **Solution** Suppose $G=\left\{ 0,1,2,3 \right\}$ i) The given table show that each element of ... }$, $a+b\in \mathbb{Z}$. b- Since $a+\left( b+c \right)=\left( a+b \right)+c$, thus associative law holds in $\mathbb{Z}$. c- Since $0\in \mathbb{Z}$ such th... ts the sums of the elements of set $\left\{ E,O \right\}$. The identity element of the set is $E$ becau
- Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
- d{array} \] As $(-1)+(-1)=-2 \notin \{0,-1\}$. $\Rightarrow \{0,-1\}$ does not satisfy closure property ... y} \] As $(-1)\times (-1)= 1 \notin \{0,-1\}$. $\Rightarrow \{0,-1\}$ does not have closure property w.r... ine \end{array} \] As $1+1=2 \notin \{1,-1\}$. $\Rightarrow \{1,-1\}$ does not closure property w.r.t. '... he entries of the table belongs to $\{1,-1\}$. $\Rightarrow \{1,-1\}$ has closure property w.r.t. '$\tim