Question Number 178448 by Spillover last updated on 16/Oct/22 $$\mathrm{Using}\:\mathrm{the}\:\mathrm{algebra}\:\mathrm{propositions} \\ $$$$\mathrm{simplify} \\ $$$$\left(\mathrm{p}\leftrightarrow\mathrm{q}\right)\rightarrow\left(\mathrm{p}\rightarrow\mathrm{q}\right) \\ $$ Answered by greougoury555 last updated on 16/Oct/22 $$\left[\left({p}\rightarrow{q}\right)\wedge\left({q}\rightarrow{p}\right)\right]\rightarrow\left({p}\rightarrow{q}\right) \\…
Question Number 178434 by Spillover last updated on 16/Oct/22 $$\mathrm{Simplify}\:\mathrm{by}\:\mathrm{using}\:\mathrm{law}\:\mathrm{of}\:\mathrm{algebra} \\ $$$$\left(\mathrm{a}\right)\:\left[\mathrm{p}\vee\left(\mathrm{p}\wedge\mathrm{q}\right)\right]\rightarrow\sim\mathrm{p} \\ $$$$\left(\mathrm{b}\right)\left(\mathrm{p}\wedge\mathrm{q}\right)\rightarrow\mathrm{q} \\ $$ Answered by Spillover last updated on 16/Oct/22 Answered by…
Question Number 178433 by Spillover last updated on 16/Oct/22 $$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{proposition}\:\mathrm{is}\:\mathrm{true}\:\mathrm{or}\:\mathrm{not} \\ $$$$\left[\left(\mathrm{p}\rightarrow\sim\mathrm{q}\right)\wedge\left(\mathrm{q}\vee\mathrm{r}\right)\wedge\mathrm{p}\right]\rightarrow\mathrm{r} \\ $$ Answered by Spillover last updated on 18/Oct/22 Terms of…
Question Number 178423 by Shrinava last updated on 16/Oct/22 $$\frac{\mathrm{m}}{\mathrm{n}}\:=\:\frac{\mathrm{k}}{\mathrm{p}}\:\:\:\mathrm{and}\:\:\:\frac{\mathrm{m}}{\mathrm{n}}\:=\:\frac{\mathrm{k}}{\mathrm{p}}\:=\:\mathrm{1},\mathrm{5} \\ $$$$\mathrm{Find}\:\:\:\frac{\mathrm{m}}{\mathrm{n}}\:+\:\frac{\mathrm{k}}{\mathrm{p}}\:=\:? \\ $$ Answered by haladu last updated on 16/Oct/22 $$\:\: \\ $$$$\:\:\frac{\boldsymbol{\mathrm{m}}}{\boldsymbol{\mathrm{n}}}\:+\:\frac{\boldsymbol{\mathrm{k}}}{\boldsymbol{\mathrm{p}}}\:\:=\:\mathrm{2}\:\frac{\boldsymbol{\mathrm{m}}}{\boldsymbol{\mathrm{n}}}\:\:=\:\mathrm{2}×\:\mathrm{1}.\mathrm{5}\:\:=\:\mathrm{3}\: \\…
Question Number 178413 by mathlove last updated on 16/Oct/22 $$\left(\mathrm{2}{x}^{\mathrm{3}} {y}+\mathrm{3}{xy}−\mathrm{5}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{12}\right)\boldsymbol{\div}\left(\mathrm{2}{x}−\mathrm{4}\right) \\ $$$$ \\ $$Divide it using compound division Commented by Rasheed.Sindhi last…
Question Number 178412 by Spillover last updated on 16/Oct/22 $$\mathrm{Express}\:\mathrm{sinh}\:^{−\mathrm{1}} \mathrm{x}−\mathrm{ln}\:\mathrm{x}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of} \\ $$$$\mathrm{natural}\:\mathrm{logarithms}.\mathrm{Hence}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{limit}\:\mathrm{as}\:\mathrm{x}\rightarrow\infty \\ $$ Answered by Ar Brandon last updated on 16/Oct/22…
Question Number 178415 by Spillover last updated on 16/Oct/22 $$\mathrm{If}\:\mathrm{acosh}\:\mathrm{x}+\mathrm{bsinh}\:\mathrm{x}=\mathrm{c}\: \\ $$$$\mathrm{show}\:\mathrm{that}. \\ $$$$\mathrm{x}=\mathrm{ln}\:\left[\frac{\mathrm{c}\pm\sqrt{\mathrm{c}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }}{\mathrm{a}+\mathrm{b}}\right] \\ $$ Answered by haladu last updated on…
Question Number 47331 by MJS last updated on 08/Nov/18 $$\mathrm{this}\:\mathrm{remained}\:\mathrm{unsolved}… \\ $$$$\mid{x}−\frac{\mathrm{3}}{\mathrm{4}}\mid×\mid{x}+\frac{\mathrm{5}}{\mathrm{4}}\mid=\mathrm{3};\:{x}\in\mathbb{C} \\ $$ Commented by MJS last updated on 08/Nov/18 $$\mid{a}−\frac{\mathrm{3}}{\mathrm{4}}+{b}\mathrm{i}\mid×\mid{a}+\frac{\mathrm{5}}{\mathrm{4}}+{b}\mathrm{i}\mid=\mathrm{3}\:\mathrm{with}\:{a},\:{b}\:\in\mathbb{R} \\ $$$$\sqrt{\left({a}−\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} +{b}^{\mathrm{2}}…
Question Number 178400 by infinityaction last updated on 16/Oct/22 $$\:\:\mathrm{evaluate}\:\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{k}\:\mathrm{e}^{\mathrm{kx}} \\ $$ Answered by mr W last updated on 16/Oct/22 $${S}=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{ke}^{{kx}}…
Question Number 178389 by cortano1 last updated on 16/Oct/22 $$\:\:\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{p}\Rightarrow\left(\left(\mathrm{p}\Rightarrow\mathrm{q}\right)\Rightarrow\mathrm{q}\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{is}\:\mathrm{tautology}\: \\ $$ Answered by Spillover last updated on 16/Oct/22 Terms of…