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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 $G$, under the given operation a group? Abelian or non-... $. This show that $0$ is the identity element. (ii) Since $1+1=0$ (identity element) so the inverse of $1$ is $1$. (iii) It is clear from table that element of the given
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... closure property w.r.t. '$\times$' **Question 1(iii)** Is the set $\{0,-1\}$ has closure property w.... roperty:** Commutative property w.r.t. '+'. ---- (ii) $(a+1)+ \frac{3}{4}= a+(1+\frac{3}{4})$ **Property:** Associative property w.r.t. '+'. ---- (iii) $(\sqrt{3}+\sqrt{5})+\sqrt{7}= \sqrt{3}(\sqrt{5}
Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
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(i^2)^4 \cdot i$ $=1 \cdot i$ =$i$. **Question 4(ii)** Simplify: $i^{14}$ **Solutions** $i^{14}$ $=(i^2)^7 $ $=(-1)^7 $ $=-1$. **Question 4(iii)** Simplify: ${-i}^{19}$ **Solutions** \begin{... *Solutions** $\sqrt{-1}b= bi$ ---- **Question 5(ii)** Write $\sqrt{-5}$ in term of $i$ **Solution... sqrt{-1}\cdot \sqrt{5} =\sqrt{5}i$ **Question 5(iii)** Write $\sqrt{-\frac{16}{25}}$ in term of $i$
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 set have identity element w.r.t. binary operation
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... rsa (i.e. cos will be converted to sin). **Step III:** Now check in which quadrant $n\cdot \frac{\pi
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
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