Question Number 47354 by behi83417@gmail.com last updated on 08/Nov/18 Commented by behi83417@gmail.com last updated on 08/Nov/18 $${ABC},{is}\:{a}\:{equelateral}\:{triangle}\:{with} \\ $$$${AB}=\mathrm{2},{and}:{AC}\:'=\mathrm{3},{BA}'=\mathrm{2}. \\ $$$$……\boldsymbol{\mathrm{CD}}=? \\ $$ Commented by…
Question Number 45840 by Rauny last updated on 17/Oct/18 $${a}\leqq\mathrm{7}\Rightarrow\mathrm{P}\left(!\exists{x}_{{a}} \right)=\mathrm{0}, \\ $$$${b}\leqq\mathrm{9}\Rightarrow\mathrm{Q}\left(!\exists{y}_{{b}} \right)=\mathrm{0}\:\mathrm{for}\:{a},\:{b}\in\mathbb{N} \\ $$$$\mathrm{And}\:{A}\supsetneq{A}':\:{A}=\left\{\left({x},\:{y}\right)\mid\mathrm{P}\left({x}\right)\centerdot\mathrm{Q}\left({y}\right)=\mathrm{0}\right\}={A}', \\ $$$${B}_{\in{A}} =\left\{\left({x},\:{y}\right)\in{A}\mid{x}={y}\right\} \\ $$$$\mathrm{Then}\:\forall{t}\in\mathbb{N}:\:\mid{B}\mid={n}\left({t}\right)={f}\left(\mathrm{P}\left({x}\right),\:\mathrm{Q}\left({y}\right)\right), \\ $$$$\mathrm{also}\:\mathrm{only}\:{t}\:\mathrm{can}\:\mathrm{be}\:\mathrm{in}\:\left[{N},\:{M}\right]. \\ $$$$\mathrm{find}\:{M}.…
Question Number 44826 by Joel578 last updated on 05/Oct/18 $$\mathrm{Let}\:{A}\:\mathrm{and}\:{B}\:\mathrm{be}\:\mathrm{sets}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:{A}\:=\:{B}\:\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if}\:{A}\:\cup\:{B}\:=\:{A}\:\cap\:{B} \\ $$ Answered by Kunal12588 last updated on 05/Oct/18 $${A}\:\cup{B}={A}\cap{B}\:……\left(\mathrm{1}\right) \\ $$$${let}\:\:{x}\in{A} \\…
Question Number 175800 by cortano1 last updated on 07/Sep/22 $$\:\mathrm{Find}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{of} \\ $$$$\:\:\mathrm{3}\:\mathrm{digits}\:\mathrm{such}\:\mathrm{that}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\:\mathrm{sum}\:\mathrm{of}\:\mathrm{3}\:\mathrm{diffrent}\:\mathrm{numbers}\:\mathrm{of} \\ $$$$\:\:\mathrm{prime} \\ $$ Answered by BaliramKumar last updated on 07/Sep/22…
Question Number 175353 by Eulerian last updated on 28/Aug/22 $$\:\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}\:=\:\mathrm{0} \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:\frac{−\mathrm{b}\pm\sqrt{\mathrm{b}^{\mathrm{2}} −\mathrm{4ac}}}{\mathrm{2a}} \\ $$$$\: \\ $$$$\:\mathrm{Example}: \\ $$$$\: \\ $$$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{equation} \\…
Question Number 42763 by Joel578 last updated on 02/Sep/18 $$\mathrm{For}\:{A}\:=\:\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3}\right\},\:\mathrm{let}\:{B}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{2}−\mathrm{element}\:\mathrm{sets} \\ $$$$\mathrm{belonging}\:\mathrm{to}\:{P}\left({A}\right)\:\mathrm{and}\:\mathrm{let}\:{C}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{consisting}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sets}\:\mathrm{that}\:\mathrm{are}\:\mathrm{intersections}\:\mathrm{of}\:\mathrm{two}\:\mathrm{distinct}\:\mathrm{elements} \\ $$$$\mathrm{of}\:{B}.\:\mathrm{Determine}\:{C} \\ $$$$ \\ $$$${P}\left({A}\right)\:=\:\mathrm{power}\:\mathrm{set}\:\mathrm{of}\:{A} \\ $$ Commented by Joel578…
Question Number 173065 by mnjuly1970 last updated on 06/Jul/22 Commented by a.lgnaoui last updated on 06/Jul/22 $$\mathrm{103} \\ $$ Commented by mr W last updated…
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Question Number 104544 by john santu last updated on 22/Jul/20 $$\mathcal{G}{iven}\:{a}_{{n}+\mathrm{1}} \:=\:\mathrm{5}{a}_{{n}} −\mathrm{6}{a}_{{n}−\mathrm{1}} \\ $$$$.\mathcal{I}{f}\:{a}_{\mathrm{1}} =\:\mathrm{10}\:{and}\:{a}_{\mathrm{2}} =\:\mathrm{26},\:{find}\:{a}_{{n}} ? \\ $$ Answered by bobhans last updated…