Can anyone provide a truth table for this logic equation?

Question

I recently cracked open my logic textbook to try to relearn some of the simple things I've forgotten. I don't usually work with logic formula, so I'm not particularly familiar with the equations or their truth tables and while I skimmed through the basics in the text some of the work questions have no real setup. I'm stumped on how to produce a truth table for the following equation: ~ ~ (p or ~p) . I made up a truth table and I think this question is just a (complicated) rendering of part of the material implication and that it is true in every instance except when p is false and ~p is true, My truth table looked like this:

p or ~p

t---t---t

f---f---t

t---t---f

f---t---f

I figured the two negations equaled the absence of any negation. Can anyone provide me with a truth table that is correct if mine is not?

Answer 1

well i would think it was...

p or ~ p

t   t   f t

f   f    f t                  

t   t   t f              

f   t   t f          but it has been two years since i have learned logic

i thought that  a f or f would result as false but its true on urs

Answer 2

Let x = ~~(p or ~p).

Reduce the logical equation to

x = p or ~p

Thus, the truth table is as follows:

p     x

--------------

t      t

f      t

Answer 3

p or ~p  is always true ( i assume the ~ stands for negation).

1    or 0   = 1

0    or 1   = 1

this is where your table ends.

because if p is 1 (true) , the non p is false (0). and if p is false, then non p is true.  p and non p can never have the same value.

where 1 = true and 0 = false.  

(for "or" only one of the two variables needs to be True, for the result to be True;   for "and"  either both of them are True, or both of them are False, for the result to be True. any other cases, the result is False)

Answer 4

p  . .~p . . .p or ~p .  .~(p or ~p) .  .~~(p or ~p)

T  . . .F . . . . .T . . . .  . . .F . . . . .. . . .T

F  . . .T . . . . .T . . . .  . . .F . . . . .. . . .T  

From the truth table above, we see that:

Proposition 'p or not p' is always TRUE because either p or not p must be TRUE.

Proposition not(p or not p) is the negation of a TRUE proposition, therefore it is FALSE

Proposition ~~(p or ~p) is a double negation, is equivalent to the proposition double-negated which is always TRUE, so it is always TRUE

              

Answer 5

You are correct the result is always true.

t or t is t

so

t--t--t