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Question
Prove the following statement by contradication method.
p: The sum of an irrational number and a rational number is irrational.
Solution
Let p is false i.e., the sum of an irrational number and a rational number is rational.
Ler `sqrt(lambda)` is irrational and n is rational number
⇒ `sqrt(lambda) + n = r` ....(Rational)
⇒ `sqrt(lambda) = r - n`
We observe that `sqrt(lambda)` is irrational where as (r – n) is rational which is a contradiction.
So, our supposition is wrong.
Hence, p is true.
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