Determine whether the argument used to check the validity of the following statement is correct :

p : " If $x^{2}$ is irrational, then x is rational "

The statement is true because the number $x^{2} = π^{2}$ is irrational, therefore $x = π^{2}$ is irrational.

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Solution

The argument used to check the validity of the given statement is not correct because it does not produce a contradiction.

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Similar questions

Write the component statement of the following compound statement and check whether the compound statement is true or false.

$\sqrt{2}$ is a rational number or an irrational number'.

x = 3 + 2 \sqrt{2}

x + \frac{1}{x}

\sqrt{3} + 3 \sqrt{2}

\sqrt{2} - \sqrt{3}

Check the validity of the statements given below by the method given against it.

(i) p: The sum of an irrational number and a rational number is irrational (by contradiction method).

(ii) q: If n is a real number with n > 3, then n² > 9 (by contradiction method).

n

n > 3

n^{2} > 9

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