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Question
Check the validity of the statements given below by the method given against it.
p: The sum of an irrational number and a rational number is irrational (by contradiction method).
Solution
The given statement is as follows.
p: the sum of an irrational number and a rational number is irrational.
Let us assume that the given statement, p, is false. That is, we assume that the sum of an irrational number and a rational number is rational.
This is a contradiction. Therefore, our assumption is wrong.
Therefore, the sum of an irrational number and a rational number is rational.
Thus, the given statement is true.
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