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Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
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s: (i) Name the identity element if it exists? (ii) What is the inverse of 1? (iii) Is the set $G$... $. This show that $0$ is the identity element. (ii) Since $1+1=0$ (identity element) so the inverse ... table is a member of $G$ thus closure law holds. ii) $\oplus$ is associative in $G$. iii) Table show... t a group w.r.t to “$\times $”. **Question # 3 (ii)** Determine whether or not the set of rational n
Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
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closure property w.r.t. '$\times$'. **Question 1(ii)** Is the set $\{1\}$ has closure property w.r.t... roperty:** Commutative property w.r.t. '+'. ---- (ii) $(a+1)+ \frac{3}{4}= a+(1+\frac{3}{4})$ **Prop... row 0<1$. **Property:** Additive property. ---- (ii) $-5<-4 \quad \Rightarrow 20>16$. **Property:** ... &= \frac{a+b}{c}=R.H.S \end{align} **Question 4(ii)** Prove the following rules of addition: $$\fra
Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
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(i^2)^4 \cdot i$ $=1 \cdot i$ =$i$. **Question 4(ii)** Simplify: $i^{14}$ **Solutions** $i^{14}$ ... *Solutions** $\sqrt{-1}b= bi$ ---- **Question 5(ii)** Write $\sqrt{-5}$ in term of $i$ **Solution... rac{-4}{65},\frac{-7}{65} \right)$ **Question 14(ii) ** Find the multiplicative inverse of complex n... \right)\left( a-2ib \right)$ ---- **Question 15(ii) ** Factorize: ${9{a}^{2}}+16{{b}^{2}}$ **Solu
Definitions: FSc Part 1 (Mathematics): PTB
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$.\\ (i) Empty set is a sub set of every set.\\ (ii) Every set is subset of itself. * **Proper su... i) it is closed under given Binary operation. \\ (ii) The Binary operation is associative. * **Mono... i) it is closed under given Binary operation. \\ (ii) The Binary operation is associative.\\ (iii) The... i) it is closed under given Binary operation. \\ (ii) The Binary operation is associative.\\ (iii) The
MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
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\ (i) $a>b \wedge b>c \Rightarrow a>c$\\ (ii) $a<b \wedge b<c \Rightarrow a<c$\\ is called ---... mathbb{R}$\\ (i) $a>b \Rightarrow a+c>b+c$\\ (ii) $a<b \Rightarrow a+c<b+c$\\ is called ----- prop
Trigonometric Formulas
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I:** First check that $n$ is even or odd. **Step II:** If $n$ is even then the answer will be in $\si
Ch 09: Fundamental of Trigonometry @fsc-part1-ptb:important-questions
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frac{1}{3}$ and the terminal arm of the angle in $II$-Quad. --- //BISE Sargodha(2016)// * Prove that