### 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.

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

- (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?

- Evaluate:

a) (10 pts) 7 mod 5

b) (5 pts) ⌈ 2.35 ⌉

- (10 pts) In the series 1, 4, 9, 16, 25, ... described by
S
_{i} = i^{2}, what is S_{9}?

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

- (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?