Question

-I need to fill in the missing row of the truth table.
-And are the two statements logically equivalent? Why please?(:

Answer 1

Let's start with the first two blank spaces, that correspond to the p column, and the q column. Can you tell me what those two spaces should be filled with?

Answer 2

I don't know what they would be

Answer 3

F, T?

Answer 4

Right. Those first two blanks should have F, and then T.

For the next column, you want ~q. In other words, the opposite of q. If you wrote T for q, what should ~q be?

Answer 5

Oh so the next one is T (~q)

Answer 6

It should actually be F for ~q.

T for q, means ~q is F.

Answer 7

Ok so now what does the ^ mean

Answer 8

For the next column, you have p\(\wedge\)q. This means that you write T when both p and q are T.

Do you have T for both p and q in this row?

Answer 9

F,T,F,F?

Answer 10

That does seem to be correct. However, in the future, please do not post repeat questions like this, especially if you have received help the previous time you asked the question.

Answer 11

Also, can you tell me if the two statements are logically equivalent now?

Answer 12

Alright im sorry.. and I don't know what the last 2 rows are still.

Answer 13

last three*

Answer 14

Sorry, afk for a bit there.

So you have FTFF for the first 4 columns. That looks perfect so far. For the next column, you have ~(p\(\wedge\)q). In other words, the opposite of p\(\wedge\)q. You had F, so therefore, the fifth column should have T.

Answer 15

So the next one will be T?

Answer 16

The fifth column will be T. After that however, you have pV~q. This means that if either p or ~q has a T, you write a T for pV~q.

However, both p and ~q have F, so you write an F in the second to last column.

Answer 17

so now wwhat does that <--> sign mean?

Answer 18

Now we just have to worry about the last column.

To fill this one in, look at the 5-th column and the 6-th column. If both the columns have the same letter in, you put a T in the last column. If they're different, you put a F.

What do you think should go in the last column?

Answer 19

T

Answer 20

I would say F. Notice that you have T in the 5th column, and F in the 6th. Therefore the final column must have an F.

Answer 21

Darn :\ So the statement is false?

Answer 22

Right. So In the end, from left to right, you should have:

FTFFTFF

Answer 23

For the last question, it asks if the statements are logically equivalent. If there is any F in the last column, they are not equivalent. Since you have to F's, the statements are not logically equivalent.