hello

they ask me to find the values for this statement
(~pvq) -> (pv~q)

for this stament I got as answer 3 true values and 1 false values, is that right?

they also ask me to find out whether this stament is a tautology

[(p->~q)^q]->~p

i got as answer that this is not a tautology

finally they ask me to by using morgan laws translate the following statement into a statement that means the same thing.

The exam was easy and I studied all night.
I studied all night then the exam was easy.

thank you.

2. Originally Posted by jhonwashington
hello

they ask me to find the values for this statement
(~pvq) -> (pv~q)

for this stament I got as answer 3 true values and 1 false values, is that right?
yes, you're right

they also ask me to find out whether this stament is a tautology

[(p->~q)^q]->~p

i got as answer that this is not a tautology
right again

finally they ask me to by using morgan laws translate the following statement into a statement that means the same thing.

The exam was easy and I studied all night.
I studied all night then the exam was easy.
you were doing so well, but this is incorrect.

recall what DeMorgan's Laws say, there are two of them (that I know of):

Law 1: $\sim (P \wedge Q) \Longleftrightarrow \sim P \vee \sim Q$

Law 2: $\sim (P \vee Q) \Longleftrightarrow \sim P \wedge \sim Q$

The statement we have is of the form $\sim P \wedge \sim Q$

That is,

$\sim P$ = "The exam was easy"

$\sim Q$ = "I studied all night"

So then,

$P$ = "The exam was hard" or if you want to be technical, "The exam was not easy"

$Q$ = "I did not study all night"

So, the answer you are looking for is:

$\sim (P \vee Q)$ = "It is not true that the exam was hard or that I did not study all night"

3. Jhevon, thanks a lot for the help!