Mathematics
Let r be a rational number and x be an irrational number. Use proof by contradiction to show that r + x is an irrational number.
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Answer
By seeking contradiction,
Let r + x is a rational number.
We know that,
Rational number can be expressed in the form of , where p, q ∈ I and q ≠ 0.
So,
From above we see,
That x is a rational number.
This is not possible as in question it is given that x is an irrational number.
Our assumption of r + x being a rational number is wrong.
Hence, proved that r + x is an irrational number.
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