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- Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
- or '$\times$'. **Solutions** Addition Table \[\begin{array}{|c|c|} \hline + & 0 \\ \hline 0 & 0 ... ure property w.r.t. '+'. Multiplication Table \[\begin{array}{|c|c|} \hline \times & 0 \\ \hline 0... or '$\times$'. **Solutions** Addition Table \[\begin{array}{|c|c|} \hline + & 1 \\ \hline 1 & 2 ... ure property w.r.t. '+'. Multiplication Table \[\begin{array}{|c|c|} \hline \times & 1 \\ \hline 1
- Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
- $G=\{0,1\}$ is shown in the adjoining table. \[ \begin{array}{|c|c|c|} \hline \oplus & 0 & 1 \\ \h... able, show that the set is an Abelian group? \[ \begin{array}{|c|c|c|c|c|} \hline \oplus & 0 & 1 &... Closure property holds in $\mathbb{Q}$ under $+$ because sum of two rational number is also rational.... is set? Show that this set is Abelian group. \[ \begin{array}{|c|c|c|} \hline \oplus & E & O \\ \
- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- lex numbers. **Solution** Let \(z,w,\) and \(v\) be complex numbers. Then the following properties ho... =z\nonumber \] - Existence of Additive Inverse \[\begin{array}{l} \mbox{For each} \; z\in \mathbb{C}, ... 4(iii)** Simplify: ${-i}^{19}$ **Solutions** \begin{align} {-i}^{19}& =[(-1)(i)] ^{19}=(-1)^{19}\... laystyle {{(-1)}^{-\frac{21}{2}}}$ **Solution** \begin{align} (-1)^{-\frac{21}{2}}&=\frac{1}{(-1)^\f