(i) Let p : the number x is not a rational number q : the number x is not an irrational number
Now ~ p : The number x is a rational number
q : The number x is a rational number (∵ when a number is not irrational, it is a rational)
~p = q and ~q = p
⇒ given pairs of statements are negations of each other.
(ii) Let p : the number x is a rational number
q : the number x is an irrational number.
Now, ~p: the number x is an irrational number (∵ When a number is not rational, it is irrational)
∴ ~p = q and ~q = p
⇒The pairs are negations of each other.