August 21st, 2020 
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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