Question

Create a truth table and prove that for any statement p, ~(~p) equals p.

Answer 1

Hey

Answer 2

Consider below statements :

1) She is a `good girl`
2) She is not a `not good girl`

Answer 3

Are they same or do you see any logical difference between them ?

Answer 4

One is saying she IS a good girl and one is saying she is NOT a good girl.

Answer 5

do you know how to prove logical statements with a truth table? or disprove?

Answer 6

Think carefully.
I think the second statement is saying "She is not a bad girl"

Answer 7

not good = bad

Answer 8

Ohhhh

Answer 9

I want you see that "not a bad girl" is logically same as "good girl"

Answer 10

Two negatives make a positive !

Answer 11

Gotcha ^_^

Answer 12

Very much like -(-3) = 3

Answer 13

Let's try constructing a truth table keeping that idea in mind

Answer 14

Do you know what a truth table is ? Have you ever seen a truth table before ?

Answer 15

Yeah I do

Answer 16

Then what's stopping you from creating one here ?

Answer 17

p ~p ~(~p)
T ? ?

Answer 18

Can you fill in the question marks ?

Answer 19

what is opposite of T ?

Answer 20

T F = T?

Answer 21

I don't get you

Answer 22

What is opposite of True ?

Answer 23

False

Answer 24

T = True
F = False

Answer 25

if \(p\) is True,
then what is the value of ~\(p\) ?

Answer 26

...True?

Answer 27

Nope, remember :

"~p" is a short cut for "not p"

Answer 28

So False.

Answer 29

aka p is not true

Answer 30

if "p" is true,
then "~p" is false

Answer 31

what about ~(~p) ?

Answer 32

~(~p) is True then...?

Answer 33

you've got it!

Answer 34

fill in the table

Answer 35

p ~p ~(~p)
T ? ?

Answer 36

p ~p ~(~p)
T F T

Answer 37

Perfect!
There is another case for "p"
it can be false

Answer 38

lets put it in another row

Answer 39

p ~p ~(~p)
T F T
F ? ?

Answer 40

See if you can fill in the question marks

Answer 41

~p is the opposite of whatever p is right? So if p was False then ~p would be True...meaning...

p ~p ~(~p)
T F T
F T F

Correct?

Answer 42

Perfect!
Now look at first and last columns. What do you notice ?

Answer 43

They are the same...both True, or both False.

Answer 44

Exactly! Can we now say that p = ~(~p) ?

Answer 45

Yes

Answer 46

Thank you so much.

Answer 47

yw, good job !