6.(i)    Check the validity of the statement 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).

Answers (1)

Assume that the given statement p is false.

The statement becomes: The sum of an irrational number and a rational number is rational.

Let  \sqrt p + \frac{s}{t} = \frac{q}{r}

Where \sqrt p is irrational number and \frac{q}{r} and \frac{s}{t} are rational numbers.

  \therefore \frac{q}{r} - \frac{s}{t} is a rational number and \sqrt p is an irrational number, which is not possible.

This is a contradiction.

Hence our assumption is wrong.

Thus, the given statement p is true.

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