Homework SourseDetermine whether any of the below three statements are equi
Determine whether any of the below three statements are equivalent or not:
S1: ~(p ^ q)
S2: ~p ^ ~q
S3: ~p v ~q
Include an argument in the form of a truth table or counterexample to support your answer. You do need not to show the intermediate steps for the truth table.
Solution
S1
P
Q
P ^ Q
~(P ^ Q)
T
T
T
F
T
F
F
T
F
T
F
T
F
F
F
T
S2
P
Q
~P
~Q
~P ^ ~Q
T
T
F
F
F
T
F
F
T
F
F
T
T
F
F
F
F
T
T
T
S3
P
Q
~P
~Q
~P V ~Q
T
T
F
F
F
T
F
F
T
T
F
T
T
F
T
F
F
T
T
T
As per the result of the above truth table:
S1 is equivalent to S3
S1 is not equivalent to S2
S2 is not equivalent S3
| S1 | P | Q | P ^ Q | ~(P ^ Q) |
| T | T | T | F | |
| T | F | F | T | |
| F | T | F | T | |
| F | F | F | T |
