Menu Close

Category: Logic

Let-n-be-an-odd-positive-integer-On-some-field-n-gunmen-are-placed-such-that-all-pairwise-distances-between-them-are-different-At-a-signal-every-gunman-takes-out-his-gun-and-shoots-the-closest-gun

Question Number 13893 by Tinkutara last updated on 24/May/17 $$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{positive}\:\mathrm{integer}.\:\mathrm{On} \\ $$$$\mathrm{some}\:\mathrm{field},\:{n}\:\mathrm{gunmen}\:\mathrm{are}\:\mathrm{placed}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{all}\:\mathrm{pairwise}\:\mathrm{distances}\:\mathrm{between} \\ $$$$\mathrm{them}\:\mathrm{are}\:\mathrm{different}.\:\mathrm{At}\:\mathrm{a}\:\mathrm{signal},\:\mathrm{every} \\ $$$$\mathrm{gunman}\:\mathrm{takes}\:\mathrm{out}\:\mathrm{his}\:\mathrm{gun}\:\mathrm{and}\:\mathrm{shoots} \\ $$$$\mathrm{the}\:\mathrm{closest}\:\mathrm{gunman}.\:\mathrm{Prove}\:\mathrm{that}: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{gunman}\:\mathrm{survives}; \\ $$$$\left(\mathrm{b}\right)\:\mathrm{no}\:\mathrm{gunman}\:\mathrm{is}\:\mathrm{shot}\:\mathrm{more}\:\mathrm{than}\:\mathrm{5} \\…

Consider-n-red-and-n-blue-points-in-the-plane-no-three-of-them-being-collinear-Prove-that-one-can-connect-each-red-point-to-a-blue-one-with-a-segment-such-that-no-two-segments-intersect-

Question Number 13891 by Tinkutara last updated on 24/May/17 $$\mathrm{Consider}\:{n}\:\mathrm{red}\:\mathrm{and}\:{n}\:\mathrm{blue}\:\mathrm{points}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{plane},\:\mathrm{no}\:\mathrm{three}\:\mathrm{of}\:\mathrm{them}\:\mathrm{being}\:\mathrm{collinear}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{one}\:\mathrm{can}\:\mathrm{connect}\:\mathrm{each}\:\mathrm{red} \\ $$$$\mathrm{point}\:\mathrm{to}\:\mathrm{a}\:\mathrm{blue}\:\mathrm{one}\:\mathrm{with}\:\mathrm{a}\:\mathrm{segment} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{no}\:\mathrm{two}\:\mathrm{segments}\:\mathrm{intersect}. \\ $$ Commented by mrW1 last updated…

Consider-the-followinge-statments-P-All-students-with-measles-stay-in-the-sick-bay-T-All-students-in-the-sick-bay-do-not-do-homework-Which-of-the-following-is-are-valid-deductions-from-the-tw

Question Number 144479 by byaw last updated on 25/Jun/21 $$ \\ $$$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{followinge} \\ $$$$\mathrm{statments} \\ $$$$\mathrm{P}:\:\mathrm{All}\:\mathrm{students}\:\mathrm{with}\:\mathrm{measles} \\ $$$$\:\mathrm{stay}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sick}\:\mathrm{bay}. \\ $$$$\mathrm{T}:\:\mathrm{All}\:\mathrm{students}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sick} \\ $$$$\:\mathrm{bay}\:\mathrm{do}\:\mathrm{not}\:\mathrm{do}\:\mathrm{homework}. \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\…

prove-p-q-and-negetion-of-q-negation-of-p-

Question Number 78671 by berket last updated on 19/Jan/20 $${prove}\:{p}\Rightarrow{q}\:{and}\:{negetion}\:{of}\:{q}\Rightarrow{negation}\:{of}\:{p} \\ $$ Answered by Rio Michael last updated on 19/Jan/20 $${to}\:{prove}\:{that}\:{p}\Rightarrow{q}\:\equiv\:{q}\:\Rightarrow\sim{p} \\ $$$$\:\:\mathrm{1}\:\:\boldsymbol{{set}}\:\boldsymbol{{up}}\:\boldsymbol{{a}}\:\boldsymbol{{truth}}\:\boldsymbol{{table}} \\ $$$${p}\:\:\:\:\:\:\:\:\:{q}\:\:\:\:\:\:\:\:\sim{p}\:\:\:\:\:\:\:\:\:\sim{q}\:\:\:\:\:\:\:\:{p}\Rightarrow{q}\:\:\:\:\:\:\:\sim{q}\:\Rightarrow\sim{p}…

A-C-is-false-B-C-A-is-false-C-B-is-truth-then-if-possible-F-is-truth-or-false-F-A-B-A-C-B-C-

Question Number 247 by 123456 last updated on 25/Jan/15 $$\mathrm{A}:\mathrm{C}\:\mathrm{is}\:\mathrm{false} \\ $$$$\mathrm{B}:\mathrm{C}\vee\mathrm{A}\:\mathrm{is}\:\mathrm{false} \\ $$$$\mathrm{C}:\mathrm{B}\:\mathrm{is}\:\mathrm{truth} \\ $$$$\mathrm{then}\:\mathrm{if}\:\mathrm{possible}\:\mathrm{F}\:\mathrm{is}\:\mathrm{truth}\:\mathrm{or}\:\mathrm{false}? \\ $$$$\mathrm{F}:\left(\mathrm{A}\wedge\mathrm{B}\right)\vee\left(\mathrm{A}\wedge\mathrm{C}\right)\vee\left(\mathrm{B}\wedge\mathrm{C}\right)\: \\ $$ Answered by prakash jain last…

let-set-S-R-let-nS-R-R-R-n-sets-of-R-n-Z-is-S-lt-nS-what-if-n-S-

Question Number 11145 by FilupS last updated on 14/Mar/17 $$\mathrm{let}\:\mathrm{set}\:{S}=\mathbb{R} \\ $$$$\mathrm{let}\:{nS}=\left\{\underset{{n}\:\mathrm{sets}\:\mathrm{of}\:\mathbb{R}} {\mathbb{R},\:\mathbb{R},\:…,\:\mathbb{R}}\right\}\:\:\:\:\:\:\:\:\:{n}\in\mathbb{Z}^{+} \\ $$$$\mathrm{is}\:\mid{S}\mid<\mid{nS}\mid? \\ $$$$\: \\ $$$$\mathrm{what}\:\mathrm{if}\:{n}=\mid{S}\mid? \\ $$ Commented by prakash jain…

hi-masters-look-at-this-thing-carefully-1-2-3-4-5-6-7-8-9-

Question Number 141087 by greg_ed last updated on 15/May/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{masters}}\:! \\ $$$$\boldsymbol{\mathrm{look}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{thing}}\:\boldsymbol{\mathrm{carefully}}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\:\mathrm{3}\:\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}\:\mathrm{6}\:\mathrm{7}\:\mathrm{8}\:\mathrm{9} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{10}\:\mathrm{11}\:\mathrm{12}\:\mathrm{13}\:\mathrm{14}\:\mathrm{15}\:\mathrm{16} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{17}\:\mathrm{18}\:\mathrm{19}\:\mathrm{20}\:…………….. \\ $$$$\:\:\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{line}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{column}}\:\boldsymbol{\mathrm{where}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\mathrm{795471}\:\boldsymbol{\mathrm{will}}\:\boldsymbol{\mathrm{appear}}\:! \\…