MAT 2143 Final: MAT2143 Final Exam 2015
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Please, read the following instructions carefully: you have 3 hours to complete this exam. Where it is possible to check your work, do so: this is a closed book exam, and no notes of any kind are allowed. The use of calculators, cell phones, pagers or any text storage or communication device is not permitted: answer all questions in the space provided after each question. Each answer requires justi cation written legibly and logically: you must convince the marker that you know why your solution is correct. Use the backs of pages if necessary. this space is reserved for the marker: Mat 2143, winter 2015: determine whether or not the relation is an equivalence relation on the set of real numbers r. x y if |x y| 4. Mat 2143, winter 2015: using the induction prove that n! Mat 2143, winter 2015: find all solutions of the following system of congruences x 2 x 6 (mod 5) (mod 11)
