What is the area of the shaded portion of the circle?
2 answers:
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If 
is true, then 
is false, which in turn means 
is true.
If is false, then is true, and so is false.
So, because
in both cases, the statement is a tautology (always 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 can only take two values, true and false. In the next column (), you would negate the value in the previous column. And so on.
It should roughly look like this:
p ... ~p ... ~(~p)
T ... F ... T
F ... T ... F
If
So, because
If you were to put this in a table, you would have one column each for
It should roughly look like this:
p ... ~p ... ~(~p)
T ... F ... T
F ... T ... F