Write the negation of the following statements and check whether the resulting statements are true,

(i) Australia is a continent.
(ii) There does not exist a quadrilateral which has all its sides equal.
(iii) Every natural number is greater than 0.
(iv) The sum of 3 and 4 is 9.

Solution:

(i) The negation of the statement is
     It is false that Australia is a continent.
This can also be rewritten as
     Australia is not a continent.
It is known that this statement is false.

(ii) The negation of the statement is
       It is not the case that there does not exist a quadrilateral which has all its sides equal.
This also means the following:
      There exists a quadrilateral which has all its sides equal.

Hence, this statement is true, because we know that square is a quadrilateral such that its four
sides are equal.

(iii) The negation of the statement is
     It is false that every natural number is greater than 0.
This can be rewritten as
     There exists a natural number which is not greater than 0.
This is a false statement.

(iv) The negation is
      It is false that the sum of 3 and 4 is 9.
This can be written as
     The sum of 3 and 4 is not equal to 9.
This statement is true.