Question

False or False is False, Not false is True. How ?

Answer 1

lets say False = 0 , True = 1 , or = + , not = ~ ,
say that we use standard algebra to prove this
so "False or False is False" could look like:
0+0=0
"Not False is True"
~0=1
which could be written as 1=1 because the function "Not" inverts things ie. 1 becomes a 0 and 0 becomes a 1

Answer 2

thats the rules in simple math.
if you only have two options, true or false.
then one has to be chosen, so that the math rules are kept.

! = not
true = true; !true = false;
false = false; !false = true;

this is also builds up over the concept of primitive computer language,
where everything consists of Ones(1) and Zeroes(0), true or false.