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Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
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cative inverse of $0$ in not in set $\mathbb{Q}$. Therefore the set of rational number is not a group w.r... $-a\in \mathbb{Q}$ such that $a+(-a)=(-a)+a=0$. Therefore the set of rational number is group under add... 3,...\}$. a- Since sum of integers is an integer therefore for $a,b\in \mathbb{Z}$, $a+b\in \mathbb{Z}$.... e table is symmetric about the principal diagonal therefore $\oplus$ is commutative. Hence $\left\{ E,O
Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib
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rt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \). Therefore, \( |z| = 5 \). =====Chapter 02: Set and Oper... well-defined. ====Methods to describe a set==== There are 3 method to describe a set ====Descriptive Me... ====Equivalent Set==== Two sets are equivalent if there exists a one-to-one correspondence between their ... forms a group because for every integer \( a \), there exists its additive inverse \( -a \), and additio
Definitions: FSc Part 1 (Mathematics): PTB
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ct collection of distinct object is called set.\\ There are three ways to describe a set.\\ * **Descri... two numbers $a$ and $b$. If $a,G,b$ are in $G.P$. Therefore $\frac{G}{a}=\frac{b}{G} \longrightarrow G^2... 1}{5},\frac{1}{7}$ are in harmonic sequence since there reciprocals $1,3,5,7$ are in $A.P$. * **Harmon
MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
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every statement is regarded as true or false and there is no other possibility is called - Propositi... of these - The symbol $\forall$ stand for - There exist - Belongs to - Such that - For ... - Belongs to - Such that - For all - There exists - Truth set of tautology in the relevant
MCQs Bank: FSc-I
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bra and Trigonometry Class XI are available here. There are fourteen (14) chapters in this book, therefore MCQs of each chapters are given on separate page. Thi
FSc Part 1 Mathematics Notes/Solutions
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SC-I), Punjab Textbook Board (PTB) Lahore.</lead> There are fourteen chapters in this book and we have wo... l License or stated otherwise. To view PDF files, there must be PDF Reader (Viewer) installed on your PC
MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
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a)=$ - $1$ - $0$ - $2$ - $-1$ - There is a nice short cut method for long division of p... =$ - $1$ - $-1$ - $w$ - $w^2$ - There are ----- basic techniques for solving a quadrati
Question Paper/Model Paper/Paper Pattern HSSC-I: BISE
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mediate and Secondary Education (BISE) in Punjab. There are lot of boards (e.g. Multan Board, Faisalabad
Old Question Papers/Model Papers HSSC-I (FSc-I): FBISE
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by Punjab Textbook Board (PTB) Lahore, Pakistan". There are two parts of the paper, one is objective and
Trigonometric Formulas
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in IVth quadrant and sin is –ive in IVth quadrant therefore answer will be in negative. i.e $\sin {{667}
Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
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ray}{l} \mbox{For each} \; z\in \mathbb{C}, \mbox{there exists}\; -z\in \mathbb{C} \mbox{ such that}\; z+