MAD 2104 Midterm: MAD 2104 FAU Exam 1S07b
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Exam # 1 math 2104h fall 2010. Directions: make sure to show work or explain how you got an answer. If using a graph from your calculator explain what steps you took to get the graph. Good luck, buena suerte, bonne chance, geluk, gl uck. Problems: given the number n = 1237694x nd the units digit x which makes this number divisible by 11, consider the following relation r on the set of natural numbers n (not the integers). R = {(n, m) n2 : n | m}. Proofs: prove the following statements: consider the functions f : a b and g : b c. set h = g f . Prove that if h is surjective, then g is surjective: prove the following by mathematical induction. Mad 2104h exam 1 fall 2010: supply a tch proof for the following argument. Don"t forget to support your statements by citing the appropriate lines: | x (cube(x) tet(x))
