Solutions
Problem 13 :
| p |
q |
p^q |
~(p^q) |
(p v q) |
~(p^q)v(p v q) |
| T |
T |
T |
F |
T |
T |
| T |
F |
F |
T |
T |
T |
| F |
T |
F |
T |
T |
T |
| F |
F |
F |
T |
F |
T |
Problem 17 :
| p |
q |
p^q |
~(p^q) |
~p |
~q |
~p^~q |
| T |
T |
T |
F |
F |
F |
F |
| T |
F |
F |
T |
F |
T |
F |
| F |
T |
F |
T |
T |
F |
F |
| F |
F |
F |
T |
T |
T |
T |
Not Equivalent
Problem 19
| p |
t |
p^t |
| T |
T |
T |
| T |
T |
T |
| F |
T |
F |
| F |
T |
F |
Equivalent
Problem 24
| p |
q |
r |
pvq |
p^r |
( pvq)v(p^r) |
(pvq)^r |
| T |
T |
T |
T |
T |
T |
T |
| T |
T |
F |
T |
F |
T |
F |
| T |
F |
T |
T |
T |
T |
T |
| T |
F |
F |
T |
F |
T |
F |
| F |
T |
T |
T |
F |
T |
T |
| F |
T |
F |
T |
F |
T |
F |
| F |
F |
T |
F |
F |
F |
F |
| F |
F |
F |
F |
F |
F |
F |
Not Equivalent
Problem 29
This computer program does not have a logical error AND it is not being run with an incomplete dataset
Problem 35
(x>-1) AND (x<=1)
Problem 42
| p |
q |
r |
~p |
~q |
~p^q |
q^r |
(~p^q)^(q^r) |
(~p^q)^(q^r) ^~q |
| T |
T |
T |
F |
F |
F |
T |
F |
F |
| T |
T |
F |
F |
F |
F |
F |
F |
F |
| T |
F |
T |
F |
T |
F |
F |
F |
F |
| T |
F |
F |
F |
T |
F |
F |
F |
F |
| F |
T |
T |
T |
F |
T |
T |
T |
F |
| F |
T |
F |
T |
F |
T |
F |
F |
F |
| F |
F |
T |
T |
T |
F |
F |
F |
F |
| F |
F |
F |
T |
T |
F |
F |
F |
F |
Contradiction
Problem 49
a. Commutative Law
b. Distributive Law
c. Negation Law
d. Identity Law
Problem 52
(~p^q)v(~p^~q)-----------------DeMorgan's Law
~p^(qv~q)----------------------Distributive Law
~p ^ t------------------Negation Law
~p ----------------------------Identity Law
Problem 54
(p^(p^~q))v(p^q)---------------DeMorgan's Law
(p^~q)v(p^q) ------------------Idempotent Law
p^(~qvq) ----------------------Distributive Law
p ^ t-------------------Negation Law
p -----------------------------Identity Law