Prove the following statement by contradiciton method
p : The sum of an irrational number and a rational number is irrational .

Explanation

Let `sqrt(a)` irrational and be be rational . Then, we have to prove that `(sqrt(a)+b)` is that irrational. If possible ,let `(sqrt(a)+b)` be rational. Then `(sqrt(a)+b)` is rational b is rational
`rArr [ (sqrt(a)+b)-b]` is rational `[ therefore` difference of rational is rational ]
`rArr sqrt(a)` is rational .
This contradiction the fact that `sqrt(a)` is irrational. Since tha contrational arises by assuming that `(sqrt(a)+b)` is rational hence `(sqrt(a)+b)` is irrational.