p -> ~q , p -> q
Are these Equivalent statements? This is my try. Please let me know if these truth tables are correct.
p -> ~q
p q p -> ~q p q p -> q
T T T T T T
T F T T F F
F T F F T F
F F T F F T
The statements are not equivalent.
Your truth tables are correct, and based on those truth tables, we can see that the two statements are not equivalent.
To explain how to determine if two statements are equivalent, we can compare the truth values of the statements for all possible combinations of truth values for the variables involved. If the truth values of the two statements are the same for every combination of truth values, then the statements are equivalent. If even one combination produces different truth values for the two statements, then they are not equivalent.
In this case, we can see that the truth values of the statements p -> ~q and p -> q differ for the combination of p=True and q=False. For p=True and q=False, p -> ~q is still True, while p -> q is False. Therefore, the two statements are not equivalent.
To summarize, the statements p -> ~q and p -> q are not equivalent based on the differences in their truth values for the specific combination of p=True and q=False.