Let a and b be real numbers such that ab ≠ 0. Then which of the following statements are true? Justify your answers.

(i) Both a and b must be zero.

(ii) Both a and b must be non-zero.

(iii) Either a or b must be non-zero.

Restate the following statements with appropriate conditions, so that they become true.

(i) If a² > b², then a > b.

(ii) If x² = y², then x = y.

(iii) If (x + y)² = x² + y², then x = 0.

(iv) The diagonals of a quadrilateral bisect each other.

Given that the product of two rational numbers is rational, and suppose a and b are rationals, what can you conclude about ab?

Given that the decimal expansion of irrational numbers is non-terminating, non-recurring, and $\sqrt{17}$ is irrational, what can we conclude about the decimal expansion of $\sqrt{17}$ ?