1) Suppose , , and are the statements shown below.

I am a loser.
This exam is easy.
I am an MCC math club member.

(a) Write the statement, “This exam is easy, but I am a loser because I am not a math club member.” in symbolic form.

(b) Write the negation of the statement in part (a) using words.

(c) Write the statement in words.

(d) Write the converse of the statement in part (c) using words.

2) Complete the following truth table.

T T T F F T F F

3) Write each of the following statements as common, everyday sentences. Do not just translate the symbols individually.

(a)

(b)

4) Let , , and .

(a) Find

(b) Find .

(c) Determine the number of relations from to .

(d) Determine the number of functions from to .

(e) Determine the number of surjections from to .

5) Perform the indicated calculations in .

(a)

(b)

(c)

6) Let and define the relation on as

(a) Is a partial order?

(b) Why or why not?

(c) Is an equivalence relation?

(d) Why or why not?

7) 12 yappy French poodles are weighted so that, when dropped from the top of a tall building, and . All twelve poodles are tossed.

(a) Determine the probability that exactly 7 poodles landed on their heads. Do not simplify your answer.

(b) Determine the probability that at most 10 poodles landed on their heads. Do not simplify your answer.

8) Determine the number of different arrangements of the letters of the word ‘arrangement’.

9) Find the term in the binomial expansion of containing .

10) Consider the following network.

(a) Find a maximal flow for the network. Show it on the graph above. What is the value of the flow?

(b) Find a minimum cut for the network. Show me…