Determine whether the argument used to check the validity of the following statement is correct-p- -If x2 is irrational- then x is rational- The statement is true because the number x2-2 is irrational- therefore x- is irrational-

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Irrational Numbers

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Question

Determine whether the argument used to check the validity of the following statement is correct:
p : "If x² is irrational, then x is rational"
The statement is true because the number x² = π² is irrational, therefore x = π is irrational.

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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'.

π

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).

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