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'.

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Solution

The component statements of the compound statement are

$p = \sqrt{2}$ is a rational number.

$q = \sqrt{2}$ is an irrational number.

Clearly, p is false and q is true, therefore compound statement is true.

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Write the component statement of the following compound statement and check whether the compound statement is true or false. √2 is a rational number or an irrational number'.

The component statements of the compound statement are p=√2is a rational number. q=√2is an irrational number. Clearly, p is false and q is true, therefore compound statement is true.

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'.

The component statements of the compound statement are

$p = \sqrt{2}$ is a rational number.

$q = \sqrt{2}$ is an irrational number.

Clearly, p is false and q is true, therefore compound statement is true.