2) Consider the following algorithm:

for i = 1 to n do

for j = 1 to i do

do something

end for

end for

We want to count how many times that the inner-loop body executes.

a) Write a summation to show how many times the inner-loop body executes.

b) Propose a closed form expression for this summation

c) What kind of proof would you use to prove your closed form expression correct?

3) Describe each of the following sets by listing its elements:

a. {x | x

b.

c.

4) Describe each of the following sets by giving a characterizing property in set-builder notation:

a. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

b. {4, 8, 12, 16, 20, ...}

5) Which of the following are neither binary nor unary operations on the given sets? (Justify)

a.

b.

c.

d.

6) What is the "set-builder" notation for intersection? }

7) What would the Venn diagram look like for intersection?