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Midterm 2

Midterm 2 - Problem Mark 1 2 3 4 5 6 7 8 9 Total MACM 101...

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Problem 1 2 3 4 5 6 7 8 9 Total Mark MACM 101 Midterm Test November 17, 2010 Last Name First Name and Initials Student No. Tutorial section or TA name NO AIDS allowed. Answer ALL questions on the test paper. Use backs of sheets for scratch work. Total Marks: 100 1. Give a deﬁnition of an equivalence relation. [10] An equivalence relation is a reﬂexive, symmetric transitive relation. 2. Give a deﬁnition of a one-to-one function. [10] Function f is one-to-one if a b ( f ( a ) = f ( b ) a = b ). 3. Let S ( x ) means “ x is a student”, F ( x ) means “ x is a faculty member”, A ( x,y ) means “ x has asked y a question”, where the domain consists with all people associated with SFU. Formulate in logic: There is a faculty member who has never been asked a question by a student. x ( F ( x ) ∧ ∀ y ( S ( y ) → ¬ A ( y,x ))) [10] 4. Use mathematical induction to prove n < 2 n for all positive in- tegers n . [15] (a) Basis case: Check the property for n = 1: 1

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Midterm 2 - Problem Mark 1 2 3 4 5 6 7 8 9 Total MACM 101...

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