You must do your own work.  Do not consult with anyone else. 

Part I  LOGIC PROBLEMS

Construct a Truth Table for:

1.  (P Q)    (Q P)

2.  (P Q) (P R) 

3.  [(P Q)    R] [(P    R) Q]

4.  [P = Q]    =    [(P Q) (Q P)]

                                          —- OVER —-

Part II  MATHEMATICAL INDUCTION

Prove using Mathematical Induction
Show all of your work.  Do not leave any steps out.  Be sure to do the base case.

5.    12  +  23  +  34  + + N(N+1)  = N(N+1)(N+2)/3,  for N   1

6.    1 + 4 + 7 + + (3N-2) = N(3N-1)/2, N   1.

7.    13  +  23  +  33  + +  N3  = [N(N+1)/2]2,  for N   1

8.  32N 1 is divisible by 8, N   1.

9.    Prove using Mathematical Induction that postage of five cents or more can be achieved by using only 2-cent and 5-cent stamps.

10.  Prove or disprove using Mathematical Induction that
S(N) = 2  +  4  +  6  + + 2N  =  (N+2)(N-1),  for N    3