Question -
Answer -
(i) p : For every positive real number x, the number (x – 1) is also positive.
The negation of the statement:
p: For every positive real number x, the number (x – 1) is also positive.
is
~p: There exists a positive real number x, such that the number (x – 1) is not positive.
(ii) q: For every real number x, either x > 1 or x < 1.
The negation of the statement:
q: For every real number x, either x > 1 or x < 1.
is
~q: There exists a real number such that neither x>1 or x<1.
(iii) r: There exists a number x such that 0 < x < 1.
The negation of the statement:
r: There exists a number x such that 0 < x < 1.
is
~r: For every real number x, either x ≤ 0 or x ≥ 1.