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

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