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

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of inequality (order properties), field, rule of fractions. These notes are based on the new Student Le... mmutative property w.r.t. '+'. ---- (ii) $(a+1)+ \frac{3}{4}= a+(1+\frac{3}{4})$ **Property:** Associative property w.r.t. '+'. ---- (iii) $(\sqrt{3}+\sqrt{... cative property. ---- (v) $a>b \quad \Rightarrow \frac{1}{a}<\frac{1}{b}$. **Property:** Multiplicative

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

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tion 4(iv)** Simplify: $\displaystyle {{(-1)}^{-\frac{21}{2}}}$ **Solution** \begin{align} (-1)^{-\frac{21}{2}}&=\frac{1}{(-1)^\frac{21}{2}}=\frac{1}{[(-1)^\frac{1}{2}]^{21}}\\ &= \frac{1}{i^{21}}=\frac{1}{(i^2)^{10}\cdot

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

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ty element. d- For $a\in {{\mathbb{Q}}^{+}}$, $\dfrac{1}{a}\in {{\mathbb{Q}}^{+}}$ such that $a\times \dfrac{1}{a}=\dfrac{1}{a}\times a=1$. Thus inverse of $a$ is $\dfrac{1}{a}$. Hence ${{\mathbb{Q}}^{+}}$ is group under add