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Exercise 2.8 (Solutions) @fsc-part1-ptb:sol:ch02
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n}&{{a}^{-1}}*\left( a*x \right)={{a}^{-1}}*b \\ \Rightarrow \,\,\,\,& \left( {{a}^{-1}}*a \right)*x={{a}^{-1}}*b\,\,\,\, \text{by associative law}\\ \Rightarrow \,\,\,\,& e*x={{a}^{-1}}*b \,\,\,\,\text{by inverse law.}\\ \Rightarrow \,\,\,\,& x={{a}^{-1}}*b\,\,\,\, \text{by identit... .}\end{align} And for \begin{align} & x*a=b \\ \Rightarrow \,\,\,\,& \left( x*a \right)*{{a}^{-1}}=b*{{a}^{-
Exercise 1.1 (Solutions) @fsc-part1-ptb:sol:ch01
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d{array} \] As $(-1)+(-1)=-2 \notin \{0,-1\}$. $\Rightarrow \{0,-1\}$ does not satisfy closure property w.r.t... y} \] As $(-1)\times (-1)= 1 \notin \{0,-1\}$. $\Rightarrow \{0,-1\}$ does not have closure property w.r.t. '... ine \end{array} \] As $1+1=2 \notin \{1,-1\}$. $\Rightarrow \{1,-1\}$ does not closure property w.r.t. '+'. ... he entries of the table belongs to $\{1,-1\}$. $\Rightarrow \{1,-1\}$ has closure property w.r.t. '$\times$'.
MCQs: Ch 01 Number Systems @fsc-part1-ptb:mcq-bank
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, b, c \in \mathbb{R}$\\ (i) $a>b \wedge b>c \Rightarrow a>c$\\ (ii) $a<b \wedge b<c \Rightarrow a<c$\\ is called ----- property. - Translative - Transiti... - For all $ a, b, c \in \mathbb{R}$\\ (i) $a>b \Rightarrow a+c>b+c$\\ (ii) $a<b \Rightarrow a+c<b+c$\\ is called ----- property. - Additional - Advantage
Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib
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th values of its variables. ===Example:=== \( p \rightarrow q \leftrightarrow (\neg q \rightarrow \neg p) \) is a tautology because its truth table shows that it is alwa... h values of its variables. ===Example:=== \( (p \rightarrow q) \land (p \lor q) \) is a contingency because i... \) and \( B = \{a, b, c\} \). A function \( f: A \rightarrow B \) could be defined as \( f(1) = a, f(2) = b, f
Multiple Choice Questions (MCQs)
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hat $\forall a, b, c \in R$ * $a<b \wedge c>0\Rightarrow ac\geq bc$ * $a<b \wedge c>0\Rightarrow ac> bc$ * $a<b \wedge c>0\Rightarrow ac< bc$ * $a>b \wedge c>0\Rightarrow ac= bc$ - Which of the following is an expression for $\sqrt{-81}-
Definitions: FSc Part 1 (Mathematics): PTB
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ble involved in it is called tautology.\\ e.g. $p\rightarrow q\leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology. * **Contradiction:** A statement which is a