Write out careful proofs, or givecounterexamples, to the following statements.(a) Show that the sum of the squares of any three consecutive integers, plusone, is divisible by 3.(b) Show that the sum of any four consecutive integers is divisible by 4.(c) A function ƒ: A → B has an inverse if and only if it is both surjectiveand injective.(d) If f is not surjective, then it is injective.(e) If g is surjective, then fog is surjective.(f) If g and fog are injective, then 9 is injective.(g) If ƒ og: R → R is decreasing, and g: R → R is decreasing, then f isdecreasing.(h) If x = R and x² < x, then x < 1.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

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Write out careful proofs, or give counterexamples, to the following statements. (a) Show that the sum of the squares of any three consecutive integers, plus one, is divisible by 3.