Q.Check the validity of the statements given below by the method given against it.

1. p: "The sum of an irrational number and a rational number is irrational." Proof by contradiction: Let x be irrational and y be rational. Suppose, for contradiction, that $x + y$ is rational, say $x + y = r$ where r is rational. Then $x = r - y$. Since r and y are both rational, and the difference of two rational numbers is always rational, $r - y$ is rational. So $x$ is rational. This contradicts our assumption that x is irrational. Hence, our supposition was false, and $x + y$ must be irrational. p is true.
2. q: "If n is a real number with n > 3, then $n^2 > 9$." Proof by contradiction: Suppose $n > 3$ but $n^2 \le 9$. …

Assume the negation of the claim, use basic algebraic facts (sum/difference of rationals is rational; squaring preserves order for positive reals) to derive a statement tha …

• Forgetting that a rational minus a rational is again rational — the key fact needed in part (i). …