Question

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

$\left(i\right)$ Australia is a continent

$\left(ii\right)$ There does not exist a quadrilateral which has all its sides equal

$\left(iii\right)$ Every natural number is greater than $0$

$\left(iv\right)$ The sum of $3\text{and}4\text{is}9$

Answer 1

$\left(i\right)$ Statement: Australia is a continent.
Negation: Australia is not a continent.
It’s true that Australia is a Continent
Hence, the resulting statement is false.

$\left(ii\right)$ Statement: There does not exist a quadrilateral which has all its sides equal.
Negation: There exist a quadrilateral which has all its sides equal.
It’s true that square is a quadrilateral which has its four sides equal.
Hence, the resulting statement is true

$\left(iii\right)$ Statement: Every natural number is greater than $0$.
Negation: Every natural number is not greater than $0$.
It’s true that every natural number is always greater than $0$
Hence, the resulting statement is false

$\left(iv\right)$ Statement: The sum of $3$ and $4\text{is}9$.
Negation: The sum of $3$ and $4$ is not equal to $9$.

$\because$ The sum of $3$ and $4\text{is}7$.
It’s true that the sum of $3$ and $4$ is not equal to $9$.
Hence, the resulting statement is true.