5

Use the pigeonhole principle to solve the following problem. LetX = {0, 1, 2, 3, 4, 5, 6}. Show that for any choice of 17 subsetsof X with cardinality at most 3, at...

Question

Use the pigeonhole principle to solve the following problem. LetX = {0, 1, 2, 3, 4, 5, 6}. Show that for any choice of 17 subsetsof X with cardinality at most 3, at least two such subsets are suchthat their elements sum up to the same number. For instance, thesubsets {1, 2, 6} and {0, 4, 5} are such that the sum of theirelements is 9.

Use the pigeonhole principle to solve the following problem. Let X = {0, 1, 2, 3, 4, 5, 6}. Show that for any choice of 17 subsets of X with cardinality at most 3, at least two such subsets are such that their elements sum up to the same number. For instance, the subsets {1, 2, 6} and {0, 4, 5} are such that the sum of their elements is 9.

Similar Solved Questions

Wnich HCI or HFcompound CH, or NH;HS er H;oCHLOH ((CHSNHHC=Ch HzC=CHzHC- ChjHjc- CHzFor each pair of compounds below , indicate- Wbrch more ecidic:OHNHzOHOHNH2N2OH5. Rank these acids from weakest t0 strongest: CF;COOH HCO;" HPO;' CH;COOH
Wnich HCI or HF compound CH, or NH; HS er H;o CHLOH ((CHSNH HC=Ch HzC=CHz HC- Chj Hjc- CHz For each pair of compounds below , indicate- Wbrch more ecidic: OH NHz OH OH NH2 N2 OH 5. Rank these acids from weakest t0 strongest: CF;COOH HCO;" HPO;' CH;COOH...
"Lo&m TVDONEMIYATOAMMLJA-}# MCVABCDDONEMI MEXAMMIN-J Ma(10)Find the arc length of the cune given by * 2tsinL % 2elcos 4,0.u4{(11) 221 Find cquation thctlese wth f0G (-2 ALand (8, A) and cccentricty(12) cquation for the hyperbule with focus (I1,.2) and asymptotes Ax - Jy 18 and 4x + 3y = 3 37) Find
"Lo& m TVDONEMIYATOAMMLJA-} # MCVABCDDONEMI MEXAMMIN-J Ma (10) Find the arc length of the cune given by * 2tsinL % 2elcos 4,0.u4{ (11) 221 Find cquation thctlese wth f0G (-2 ALand (8, A) and cccentricty (12) cquation for the hyperbule with focus (I1,.2) and asymptotes Ax - Jy 18 and 4x + 3y...
Wire which Is of the same length and material Js wire has twice the diameter of wire resistance of wire B Is R, what the resistance of wire A?If the0, 2R C. R/z D. 4R R/AIf you bring positively charged Insulator near two uncharged metalllic then spheres that are separate the spheres, the sphere on the right will have no net charge; positive charge: negative charge. D. either positive or negative charge: None of these correctcontact and
Wire which Is of the same length and material Js wire has twice the diameter of wire resistance of wire B Is R, what the resistance of wire A? If the 0, 2R C. R/z D. 4R R/A If you bring positively charged Insulator near two uncharged metalllic then spheres that are separate the spheres, the sphere o...
Using standard potentials given in the appendices, calculate the standard cell potentials and the equilibrium constants for the following reactions: Cu(s)+ 2Ag' (aq) Cu" (aq) 2Ag(s)Zn(s) + Fe" (aq)Zn" '(aq) +Fe(s)
Using standard potentials given in the appendices, calculate the standard cell potentials and the equilibrium constants for the following reactions: Cu(s)+ 2Ag' (aq) Cu" (aq) 2Ag(s) Zn(s) + Fe" (aq) Zn" '(aq) +Fe(s)...
E6.3 Show first that: (a) the solution =(t) of the biomolecular reaction in the previous exercise (E6.2) is:~(t) =x(O)w(o)( 1 elxo)-w(O)Jt ")/(w(o) x(O )elvo)-"(Ok )(6.74)Then Solve for x(t) . w(t), z(t) for equal initial concentrations of the reactants X Y Show that if w(0)>>x(o) the bimolecular reaction can be approximated by monomolecular reaction: Hint: the rate constants of this nonlinear reaction are dependent on the ICs_
E6.3 Show first that: (a) the solution =(t) of the biomolecular reaction in the previous exercise (E6.2) is: ~(t) =x(O)w(o)( 1 elxo)-w(O)Jt ")/(w(o) x(O )elvo)-"(Ok ) (6.74) Then Solve for x(t) . w(t), z(t) for equal initial concentrations of the reactants X Y Show that if w(0)>&...
What is the percent yield if 13.5 g SOz are obtained from the reaction of 21.3 g of 0z with 28.6 g of ZnS according to the following equation? 2 ZnS (s) 3 0z (g) 3 2 ZnO (s) + 2 SOz (g)of KCl if 1.043 g of KC] are produced from the reaction of 2.112 g 3. Calculate the percent yield the following reaction. ofKCO3 with 135 mL of0.255 MHCI according to 2 KCI COz HzO KCOz 2 HCI
What is the percent yield if 13.5 g SOz are obtained from the reaction of 21.3 g of 0z with 28.6 g of ZnS according to the following equation? 2 ZnS (s) 3 0z (g) 3 2 ZnO (s) + 2 SOz (g) of KCl if 1.043 g of KC] are produced from the reaction of 2.112 g 3. Calculate the percent yield the following re...
Point) Assuming that the buyer financed the purchas with 30-year fixed loan of Lo dollan AH mterest rale determine eloserl-form expresion for the buyer monthly principal-and-interest pAyment Hint: The interest fixed-interest loan ol this sort ACcrues monthly, so that Le-! WL ,with Lu corresponding t0 the outstanding lOaH balance conditions are Lo (initial loan AmOunt) and LzmHOHt hThe boundary(0.25 points) Ux the formula You derived in part (a) t0 determine this prineipal-And- interest payment
point) Assuming that the buyer financed the purchas with 30-year fixed loan of Lo dollan AH mterest rale determine eloserl-form expresion for the buyer monthly principal-and-interest pAyment Hint: The interest fixed-interest loan ol this sort ACcrues monthly, so that Le-! WL , with Lu corresponding ...
Tha Usa numode I } W inionation 1 8 041 4ollolomond 1 rogion
Tha Usa numode I } W inionation 1 8 041 4 ollolomond 1 rogion...
In assignment 2, we derived the following difference equation for the allele frequency in population with migration: 5A6+1) = 546n) 10Find the general solution of this difference equation: Find the solution of the difference equation subject to the initial condition fA(0) = 0.8 Describe the long- -term behaviour of the A allele frequency; in the case that fA(0) = 0.8 Which initial allele frequencies fA(0), if any, result in the A allele frequency increasing over time?
In assignment 2, we derived the following difference equation for the allele frequency in population with migration: 5A6+1) = 546n) 10 Find the general solution of this difference equation: Find the solution of the difference equation subject to the initial condition fA(0) = 0.8 Describe the long-...
Find antiderivatives of the given functions.$$f(y)= rac{5}{4}(1-y)^{1 / 4}(-1)$$
Find antiderivatives of the given functions. $$f(y)=\frac{5}{4}(1-y)^{1 / 4}(-1)$$...