If p is true, then ~p is false. The sign ~(~p) implies the statement "~p is false" is false. So, we deserve to say that ~(~p) implies p is true.

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

If p is false, then ~p is true. The authorize ~(~p) implies the statement "~p is true" is false. So, we can say that ~(~p) indicates p is false.

The compelled truth table is

p ~p ~(~p)

T F T

F T F

From the above fact table it is clear that

~(~p) = p

Hence proved.

Truth worth of ~(~p) is exact same as the reality value of p.

Step-by-action explanation:

For any kind of statement p the truth table for p, ~p and ~(~p) will be as the number attached. In this table we recognize that If truth value for p is true then ~p will be false and also ~(~p) will be true which is same truth value as truth value of p.

Now if the truth value of any kind of statement is false then fact value for ~p will certainly be true and for ~(~p) will be false which is aacquire similar to the statement p.

Hence fact value of any statement p is equivalent to the reality value of ~(~p).

Answer from: krlx

If is true, then is false, which in turn implies is true.If is false, then is true, and so is false.So, bereason in both situations, the statement is a tautology (constantly true).If you were to put this in a table, you would have one column each for . In the first column () you can think of as an independent variable that deserve to just take 2 worths, true and also false. In the next column (), you would certainly negate the worth in the previous column. And so on.It should roughly look choose this:p ... ~p ... ~(~p)T ... F ... TF ... T ... F

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