School

York UniversityDepartment

Electrical Engineering and Computer ScienceCourse Code

EECS 1019Professor

Jarek GryzStudy Guide

MidtermThis

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MATH/EECS 1019 (Fall 2016)

Test 2

Instructions:

• The exam is 80 minutes long

• You cannot use books, notes, cell phones or any other materials

• Please write your answers next to the questions and not on a separate sheet of

paper (you can use additional sheets for your own calculations)

Questions 1-11 are worth 1 point each.

1. Suppose f N → N has the rule f(n) = 4n + 1. Determine whether f is 1-1.

Ans: Yes.

2. Suppose f N → N has the rule f(n) = 4n + 1. Determine whether f is onto

N.

Ans: No.

3. Suppose f Z → Z has the rule f(n) = 3n2 − 1. Determine whether f is 1-1.

Ans: No.

4. Suppose f Z → Z has the rule f(n) = 3n − 1. Determine whether f is onto

Z.

Ans: No.

In the questions below suppose g A → B and f B → C where A = B = C = 1234, g =

(14)(21)(31)(42) and f = (13)(22)(34)(42).

5. Find f g.

Ans: (12)(23)(33)(42).

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