Question Number 4196 by Rasheed Soomro last updated on 31/Dec/15 $$\:\:\mathrm{Q}#\mathrm{4140}\:\mathrm{is}\:\mathrm{again}\:\mathrm{asked}\:\mathrm{with}\:\mathrm{following}\:\mathrm{changes}: \\ $$$$\boldsymbol{\mathrm{a}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{b}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{b}}\right), \\ $$$$\boldsymbol{\mathrm{b}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{c}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{c}}\right), \\ $$$$\boldsymbol{\mathrm{c}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{d}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{d}}\right),\: \\ $$$$\boldsymbol{\mathrm{d}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{a}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{a}}\right), \\ $$$$\mathrm{where}\:\boldsymbol{\mathrm{a}}',\boldsymbol{\mathrm{b}}',\boldsymbol{\mathrm{c}}'\:\mathrm{and}\:\boldsymbol{\mathrm{d}}'\:\mathrm{are}\:\mathrm{midpoints}\:\mathrm{of}\:\mathrm{line} \\ $$$$\mathrm{segments}\:\boldsymbol{\mathrm{ab}},\:\boldsymbol{\mathrm{bc}},\:\boldsymbol{\mathrm{cd}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{da}}\:\mathrm{respectively}. \\ $$…
Question Number 134948 by rexford last updated on 08/Mar/21 Commented by bobhans last updated on 09/Mar/21 $$\mathrm{what}\:\mathrm{definition}\:\overset{\rightarrow} {\mathrm{a}}\wedge\overset{\rightarrow} {\mathrm{b}}\:? \\ $$ Commented by rexford last…
Question Number 134689 by benjo_mathlover last updated on 06/Mar/21 $$\:\frac{\mathrm{2}^{\mathrm{289}} +\mathrm{1}}{\mathrm{2}^{\mathrm{17}} +\mathrm{1}}\:=\:\mathrm{2}^{{a}_{\mathrm{1}} } \:+\:\mathrm{2}^{{a}_{\mathrm{2}} } \:+\:\mathrm{2}^{{a}_{\mathrm{3}} } \:+\:…\:+\:\mathrm{2}^{{a}_{{k}} } \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}. \\ $$ Answered by…
Question Number 69116 by ~ À ® @ 237 ~ last updated on 20/Sep/19 $$\:{Here}\:\:{are}\:{three}\:{propositions}:\: \\ $$$$−\:{This}\:{sentence}\:{has}\:{exactly}\:{six}\:{words} \\ $$$$−{There}\:{are}\:{two}\:{wrong}\:{propositions} \\ $$$$−{The}\:{two}\:{previous}\:{sentences}\:{are}\:{correct} \\ $$$$ \\ $$$${Among}\:{that}\:{propositions}\:,{how}\:{many}\:{are}\:{wrong}?\:{list}\:{them}!…
Question Number 68695 by fermat last updated on 15/Sep/19 $${pour}\:\mathrm{1}<{k}<{n}\:\:\:\:\:{montrer}\:{que} \\ $$$${k}\left({n}+\mathrm{1}−{k}\right)<\left({n}+\mathrm{1}/\mathrm{2}\right)^{\mathrm{2}} \\ $$ Answered by mind is power last updated on 15/Sep/19 $${n}+\mathrm{1}−{k}<{n}+\frac{\mathrm{1}}{\mathrm{2}} \\…
Question Number 67651 by ~ À ® @ 237 ~ last updated on 29/Aug/19 $$\left.\mathrm{1}\right){Let}\:{consider}\:\:{S}=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:{n}\:\:\:\:\:{and}\:\:{T}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} {n} \\ $$$$\left.{W}\left.{e}\:{know}\:{that}\:\:\forall\:{x}\in\right]−\mathrm{1};\mathrm{1}\right] \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty}…
Question Number 1689 by 123456 last updated on 31/Aug/15 $$\mathrm{if}\:{p}\:\mathrm{and}\:{q}\:\mathrm{are}\:\mathrm{two}\:\mathrm{afirmation} \\ $$$$\sim\left({p}\rightarrow{q}\right)=? \\ $$$$\sim\left({p}\leftarrow{q}\right)=? \\ $$$$\sim\left({p}\Leftrightarrow{q}\right)=? \\ $$ Answered by 112358 last updated on 01/Sep/15…
Question Number 1656 by Rasheed Soomro last updated on 29/Aug/15 $$\mathrm{Let}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{are}\:\mathrm{three}\:\mathrm{statments}.\: \\ $$$$\left(\mathrm{A}\Rightarrow\mathrm{B}\Rightarrow\mathrm{C}\Rightarrow\mathrm{A}\right)\:\overset{?} {\Rightarrow}\left(\mathrm{C}\Rightarrow\mathrm{B}\right)\: \\ $$$$\left(\mathrm{A}\Rightarrow\mathrm{B}\Rightarrow\mathrm{C}\Rightarrow\mathrm{A}\right)\:\overset{?} {\Rightarrow}\left(\mathrm{B}\Rightarrow\mathrm{A}\right)\: \\ $$$$\mathrm{Prove}\:\mathrm{or}\:\mathrm{disprove}. \\ $$ Commented by Yozzian last…
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Question Number 1047 by 112358 last updated on 23/May/15 $${Simplify}\:{the}\:{following} \\ $$$${expression}\:{using}\:{the}\:{laws}\:{of}\: \\ $$$${Boolean}\:{algebra}: \\ $$$$\left({x}\wedge\backsim{y}\right)\vee\left(\backsim{y}\wedge\backsim{z}\right)\vee\left(\backsim{x}\wedge\backsim{z}\right)\:. \\ $$$$ \\ $$ Commented by prakash jain last…