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Given-a-set-consisting-of-22-integer-A-a-1-a-2-a-11-Show-that-exist-subset-of-S-with-properties-1-for-every-i-1-2-3-11-have-least-one-between-a-i-or-a-i-element-of-S-2-the




Question Number 153458 by liberty last updated on 07/Sep/21
Given a set consisting of 22 integer   A={±a_1 ,±a_2 ,...,±a_(11) }. Show that  exist subset of S with properties  (1) for every i=1,2,3,...,11    have least one between a_i  or −a_i    element of S  (2)the sum all possible numbers  in S divisible by 2015
$${Given}\:{a}\:{set}\:{consisting}\:{of}\:\mathrm{22}\:{integer} \\ $$$$\:{A}=\left\{\pm{a}_{\mathrm{1}} ,\pm{a}_{\mathrm{2}} ,…,\pm{a}_{\mathrm{11}} \right\}.\:{Show}\:{that} \\ $$$${exist}\:{subset}\:{of}\:{S}\:{with}\:{properties} \\ $$$$\left(\mathrm{1}\right)\:{for}\:{every}\:{i}=\mathrm{1},\mathrm{2},\mathrm{3},…,\mathrm{11}\: \\ $$$$\:{have}\:{least}\:{one}\:{between}\:{a}_{{i}} \:{or}\:−{a}_{{i}} \\ $$$$\:{element}\:{of}\:{S} \\ $$$$\left(\mathrm{2}\right){the}\:{sum}\:{all}\:{possible}\:{numbers} \\ $$$${in}\:{S}\:{divisible}\:{by}\:\mathrm{2015} \\ $$
Commented by talminator2856791 last updated on 07/Sep/21
 please phrase the question better.
$$\:\mathrm{please}\:\mathrm{phrase}\:\mathrm{the}\:\mathrm{question}\:\mathrm{better}. \\ $$

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