Question

@jim_thompson5910 I definitely need your help on this one.

Answer 1

what goes in the first two boxes (the left most boxes)?

Answer 2

So far I'm thinking "F" for the 1st box and "T" for the 2nd box..

Answer 3

correct

Answer 4

those set up the truth values of P and Q

Answer 5

P = false
Q = true

Answer 6

so ~P = ???

Answer 7

notP , so not false,
therefore,

T

Answer 8

so what is the truth value of ~P ^ Q

Answer 9

T?

Answer 10

yes since both ~P = true and Q = true

Answer 11

how about ~P v Q

Answer 12

not false or this is true:

T

Answer 13

So

(~P ^ Q) = true
(~P v Q) = true

Answer 14

what is the truth value of (~P ^ Q) <--> (~P v Q)

Answer 15

T as well :D

Answer 16

correct

Answer 17

that's all for part 1

Answer 18

So it should look like this:
F , T , T , T, T, T ?

Answer 19

yes

Answer 20

I want to say they are logically equivalent..

Answer 21

why?

Answer 22

Because we've proven what you stated earlier:
(~P ^ Q) = true
(~P v Q) = true

Answer 23

but is (~P ^ Q) = (~P v Q) for EVERY possible truth combination for P and Q?

Answer 24

that's what it means to be equivalent

Answer 25

Unless they're asking if "^" and "v" are equivalent, which they are NOT

Answer 26

that is true, but look at the table

Answer 27

notice in the top row

(~P ^ Q) = false
(~P v Q) = true

so (~P ^ Q) <--> (~P v Q) is false

Answer 28

Aha! Yes, I see!

Answer 29

^Ah, so this states why they are not logically equivalent, correct?

Answer 30

yes this table helps you see quickly whether or not they are equivalent

Answer 31

@jim_thompson5910 Could you delete your 2nd to last comment? I want to re-write it out.

Answer 32

huh? what do you mean?

Answer 33

Could you delete the comment that says "any point where" please?

Answer 34

-So let me try to "re-explain" this , ahahah- thanks!

Answer 35

(I sent it through the messaging feature on the website, I've made the explanation more formal, however I wanted to make sure I understood the general concept..)

Answer 36

Yeah I sent you a message

Answer 37

Thank you sooo soo much! :DD

Answer 38

no problem