MATH130: Quiz 2

Name:
You may use a calculator on this quiz. If you get stuck on a question, move on to the next. If you have time left over at the end of the quiz, check your work. There are questions on both sides of this page.

  1. (20 pts) If X = {1, 2, 3} and Z = {a, b}, what is X × Z?

     

     

     

     

     

     

  2. (15 pts) Is the set f = {(1,c), (2,d), (3,a)} a function from X = {1, 2, 3} to Y = {a, b, c, d}? Why or why not?

     

     

     

     

     

  3. Evaluate:
    a) (10 pts) 7 mod 5

     

     

     

    b) (5 pts) ⌈ 2.35 ⌉

     

     

     

  4. (10 pts) In the series 1, 4, 9, 16, 25, ... described by Si = i2, what is S9?

     

     

     

     

     

  5. (20 pts) Compute Σ i². (Start i at 1 and go up to i=4)

     

     

     

     

     

  6. (20 pts) Define R to be the (binary) relation on X = {1, 2, 3} described by R = {(1,1), (1,2), (2,2), (2,3)}. Draw the relational matrix for R.

     

     

     

     

     

     

     

Bonus: (5 pts) Is the relation R described above transitive? Why or why not?