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  • Prove the following statement by contradiction method.

Prove the following statement by contradiction method.

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

Answers (1)

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

We know that the sum of a rational no. & a irrational no. is irrational, p is false.

Let, n\rightarrow rational \; no.

& \sqrt{\lambda }\rightarrow irrational\; no.

Now,

\sqrt{\lambda }+n=r

\sqrt{\lambda }=r-n

But since, \sqrt{\lambda } is irrational and n is rational viz.contradictiona, our assumption will be false.

Thus, P is true. 

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