Q.Write the negation of the following statements.

The negation of a statement $p$, written $\sim p$, is the statement "It is false that $p$" (or, equivalently, "not $p$").

1. $p$: "Both the diagonals of a rectangle have the same length." $\sim p$: "It is false that both the diagonals of a rectangle have the same length," which can also be phrased as "The diagonals of a rectangle do not have the same length."
2. $p$: "$\sqrt{7}$ is rational." $\sim p$: "It is false that $\sqrt{7}$ is rational," i.e., "$\sqrt{7}$ is not rational" (equivalently, "$\sqrt{7}$ is irrational").
   ✓Final answer

   (i) It is false that both diagonals of a rectangle have the same length. (ii) $\sqrt{7}$ is not a rational number.

Prefix the statement with "It is false that ...", or insert "not" at the natural place in the sentence, so the resulting sentence is true exactly when the original is false.

• Writing a different, unrelated statement instead of the strict logical opposite (e.g., negating "$\sqrt7$ is rational" as "$\sqrt7$ is an integer").
• For compound descriptions like "both diagonals ... same length", carelessly negating only part of the sentence rather than the whole claim.