Check the validity of the statements given below by the method given against it.
(i) p: The sum of an irrational number and a rational number is irrational (by contradiction method).
(ii) q: If n is a real number with `n gt 3`, then `n^(2)gt9` (by contradiction method).

Explanation

(i) let `sqrt(a)` is irrational and b is a rational number.
their sum `=b+sqrt(a)`
let it is irratinal, then `b+sqrt(s)=(p)/(q)` where p and q are prim numbers.
`rArrsqrt(a)=(p)/(q)-b`
Now L.H.S. is irrational and R.H.S. is a rational number which is not possible.
Thus, the sum of a rational and an irratiaonal number is an irrational number:
`rArr` Given statement is true.
Let `ngt3` and `n^2le9`
`n=3+a`
`rArrn^2=9+a^2+6arArrn^2=9+a(a+6)`
`rArrn^2gt9` which is a contradication.
if `ngt3`, then `n^2gt9`.