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- MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
- given at the end of the page. ====MCQs==== - A well defined collection of distinct objects is calle... or membership of a set is - $\forall$ - $\wedge$ - $<$ - $\in$ - If every element of... se - If $A$ is a subset of $B$ then $A=B$, then we say that $A$ is an - Proper subset of $B$ ... se - If $p$ and $q$ are two statements then $p \wedge q$ represents - Conjunction - Disjunct
- 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:** A set is generally described as a well-defined collection of distinct objects or a well-defined object collection of distinct object is ca
- 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 ... onal numbers. ===Example=== \( \pi \) (pi) is a well-known non-terminating, non-recurring decimal. I... 2: Set and Operations===== ====Set==== A set is a well-defined collection of distinct objects or eleme... , \ldots\} \), where each element is distinct and well-defined. ====Methods to describe a set==== The
- MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
- - $\displaystyle{\frac{p}{q}}$ where $p,q \in z \wedge q \neq 0$ - $\displaystyle{\frac{q}{p}}$ where $p,q \in z \wedge q \neq 0$ - $\displaystyle{\frac{p}{q}}$ where $p,q \in Z \wedge q = 0$ - $\displaystyle{\frac{q}{p}}$ where $p,q \in N \wedge q \neq 0$ - $\mathbb{R}=$ - $\mathbb{Q}
- 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 $A,B\in G$, $AB \ne BA$
- Multiple Choice Questions (MCQs)
- mbers is that $\forall a, b, c \in R$ * $a<b \wedge c>0\Rightarrow ac\geq bc$ * $a<b \wedge c>0\Rightarrow ac> bc$ * $a<b \wedge c>0\Rightarrow ac< bc$ * $a>b \wedge c>0\Rightarrow ac= bc$ - Which of the following is an e
- 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
- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- <panel> **Question 13 ** Prove that the sum as well as the product of any two conjugate complex num... ext{ as } x, y \in \mathbb{R}. \end{align} Hence, we proved that sum as well as the product of any two conjugate complex number is a real number. </panel
- Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
- {ak}{bk}, k\neq 0\right)$ </panel> </col></grid> <well> **Book:** \\ Exercise 1.1: Textbook of Algebra... ou remix, transform, or build upon the material, you may not distribute the modified material. </well>
- 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
- Ch 02: Functions and Groups @fsc-part1-ptb:important-questions
- Sargodha(2015)// * Write the set $\{x|x \in Q \wedge x^2=2\}$ in descriptive and tabular form ---