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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 give
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... ersa (i.e. cos will be converted to sin). **Step III:** Now check in which quadrant $n\cdot \frac{\pi }{2}\pm \theta $ is lying if it is in Ist or IInd quadrant the answer will be positive as sin is positive in these quadrants and if it is in the IIIrd or IVth quadrant the answer will be negative.\
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