The negation of the statement:
Banglore is the capital of Karnataka.
is
Banglore is not the capital of Karnataka.
The negation of the statement:
It rained on July 4,2005.
is
It did not rain on July 4, 2005.
The negation of the statement:
Ravish is honest.
is
Ravish is not honest.
The negation of the statement:
The earth is round.
is
The earth is not round.
The negation of the statement:
The sun is cold.
is
The sun is not cold.
The negation of the statements:
All birds sing.
is
Not all birds sing.
The negation of the statements:
Some even integers are prime.
is
No even integers is prime.
The negation of the statements:
There is a complex number which is not a real number.
is
All complex numbers are real numbers.
The negation of the statements:
I will not go to school.
is
I will go to school.
The negation of the statements:
Both the diagonals of a rectangle have the same length.
is
There is at least one rectangle whose both diagonals do not have the same length.
The negation of the statements:
All policemen are thieves.
is
No policemen is thief.
(i) The number x is not a rational number.
⇒ The number x is an irrational number.
∴ The statement “The number x is not an irrational number." is a negation of the first statement.
(ii) The number x is not a rational number.
⇒ The number x is an irrational number.
The statement "The number x is an irrational number” is not a negation of the first statement.
(i)
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)
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)
The negation of the statement:
r: There are exists a number x such that 0 < x <1.
is
~r: For every real number x, either x ≤ or x ≥ al.
The negation of the statement:
a + b = b + a is true for every real number a and b.
is
There exist real numbers a and b for which a + b ≠ b + a.
So, the given statement is not the negation of the first statement.