EECS 1028 Discrete Math for Engineers - York University. Winter 2018 Final examination

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EECS 1028 Discrete Math for Engineers - York University MATH/EECS 1028 Winter 2018 Final examination MATH/EECS 1028 Final exam 1. (1 point) Is the following statement true? ffφgg ⊂ fφ; fφgg ... 2. (2 points) Write down the power set of f;; ffφggg. 3. (2 points) Enumerate the set fa; bg × fφ; fφgg. 4. (3 points) Suppose that A; B; C are sets and g : A ! B and f : B ! C are one-to-one functions. Show that f ◦ g is also one-to-one. MATH/EECS 1028 Final examination page 3 of 12 5. (2 points) Evaluate nXi =1 nX k =1 4ik: 6. (3 points) Is the set of all binary strings that contain no 1’s countable? Justify your answer. 7. (2 points) If A is an uncountable set and B is a countable set, prove that A - B is uncountable. MATH/EECS 1028 Final examination page 4 of 12 8. (2 points) What are the values of x for which (2x + 3)(x - 7) < 0? 9. (4 points) Prove that among any given 11 positive integers, there are always two whose difference is divisible by 10. 10. (3 points) Prove that if x is irrational then 1= [Show More]

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