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# 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

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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...
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##### 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_
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##### 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
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##### Find antiderivatives of the given functions.$$f(y)= rac{5}{4}(1-y)^{1 / 4}(-1)$$
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