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

For each statement we form the negation and then check its truth value against known facts.

1. $p$: "Australia is a continent." (This is true.) $\sim p$: "Australia is not a continent." Since $p$ is actually true, $\sim p$ is false.
2. $p$: "There does not exist a quadrilateral which has all its sides equal." (This is false — a square/rhombus is a counter-example.) $\sim p$: "There exists a quadrilateral which has all its sides equal." This is true (e.g., a square).
3. $p$: "Every natural number is greater than 0." (This is true.) $\sim p$: "There exists a natural number which is not greater than 0." Since $p$ is true, $\sim p$ is false. …

Form the negation as "It is false that ..." or by inserting/removing "not". Then evaluate the negation on its own merits — if the original s …

• Assuming a negation is automatically true without checking the actual fact.
• Negating "there does not exist" incorrectly — the negation of "there does not exist an X with proper …