Prove the following statement by contradiction method.

Question:

 Prove the following statement by contradiction method.

p: The sum of an irrational number and a rational number is irrational

Solution:

Let p is false, as the sum of an irrational number and a rational number is irrational.

Let √λ is irrational and n is rational number

√λ + n = r

√λ = r – n

But, we know that √λ is irrational whereas (r-n) is rational which is contradiction.

Here, Our Assumption is False

Hence, P is true.

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