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Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02

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0 & 3 & 0 & 1 & 2 \\ \hline \end{array} \] **Solution** Suppose $G=\left\{ 0,1,2,3 \right\}$ i) The ... number form groups with respect to $\times$. **Solution** As $0\in \mathbb{Q}$, multiplicative inverse ... ional number form groups with respect to $+$. **Solution** a- Closure property holds in $\mathbb{Q}$ und... l number form groups with respect to $\times$. **Solution** a- Since for $a,b\in {{\mathbb{Q}}^{+}}$, $ab\

Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01

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properties used in the following inequalities: **Solution** (i) $-3<-2 \quad \Rightarrow 0<1$. **Property... $$\frac{a}{c}+\frac{b}{c} = \frac{a+b}{c}$$. **Solution** \begin{align} L.H.S &= \frac{a}{c}+\frac{b}{c}... $$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$$. **Solution** \begin{align} L.H.S &= \frac{a}{b}+\frac{c}{d}... \frac{7}{12}-\frac{5}{18}=\frac{-21-10}{36}$$. **Solution** \begin{align} L.H.S &= -\frac{7}{12}-\frac{5}{

Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01

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fy the addition properties of complex numbers. **Solution** Let \(z,w,\) and \(v\) be complex numbers. Then... lify: $\displaystyle {{(-1)}^{-\frac{21}{2}}}$ **Solution** \begin{align} (-1)^{-\frac{21}{2}}&=\frac{1}{(