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- Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib
- by Punjab Textbook Board (PTB) Lahore, Pakistan. We are very thankful to [[:people:aurang-zaib]] for ... ments under consideration. ===Example:=== * If we are considering the set of all integers, then the... instances or observations. ===Example:=== * If we observe that a coin is heads-up five times in a row, we might induce that it will always land heads-up, w
- Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
- belian? **Solutions**\\ (i) From the given table we have $0+0=0$ and $0+1=1$. This show that $0$ is ... )=(-a)+a=0$. Thus inverse of $a$ is $-a$. Hence, we conclude that set of integers form groups with re... roup. For $A\in P(S)$ where A is a subset of $S$ we have $S\in P(S)$ such that $A\cap S=S\cap A=A$. ... G$ such that $A{{A}^{-1}}={{A}^{-1}}A=I$. v) As we know for any two matrices $A,B\in G$, $AB \ne BA$
- Definitions: FSc Part 1 (Mathematics): PTB
- Textbook Board (PTB) Lahore, Pakistan are given. We are very thankful to **Muhammad Waqas Sulaiman** ... sent irrational number.\\ e.g. $\pi = 3.1415...$, we don’t have exact decimal representation of this n... ...\}$ * **Set-builder method:** In this form, we use a letter or symbol for an arbitrary element o
- MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
- - Both $A$ and $B$ - None of these - If we solve $ax^2+bx+c=0$ by complete square method, we get - Cramer's rule - De Morgan's Law -... n two $2$nd degree equations then by subtraction, we get - Non-linear equation - Linear equati
- Question Paper/Model Paper/Paper Pattern HSSC-I: BISE
- /Paper Pattern HSSC-I: BISE ====== On this page, we have discussed the paper pattern of the HSSC-I or
- Definitions and Review
- The book has total of 14 chapters. On this page, we have posted material related to definitions, revi
- Definitions: Mathematics 11: PTB by Muzzammil Subhan
- by Punjab Textbook Board (PTB) Lahore, Pakistan. We are very thankful to [[:people:muzzammil-subhan]]
- FSc Part 1 Mathematics Notes/Solutions
- ead> There are fourteen chapters in this book and we have work hard to make easy and suitable solution
- MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
- se - If $A$ is a subset of $B$ then $A=B$, then we say that $A$ is an - Proper subset of $B$
- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- ext{ as } x, y \in \mathbb{R}. \end{align} Hence, we proved that sum as well as the product of any two