Find the component statements of the following and check whether they are true or not.
$\sqrt{2}$ is a rational number or an irrational number.
$\sqrt{2}$ is a rational number or an irrational number.
(N/A) The component statements are:
$p: \sqrt{2}$ is a rational number.
$q: \sqrt{2}$ is an irrational number.
The first statement $p$ is false,as $\sqrt{2}$ cannot be expressed in the form $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$.
The second statement $q$ is true.
Since the connecting word is 'or',the compound statement is true if at least one of the component statements is true. Therefore,the compound statement is true.
$p: \sqrt{2}$ is a rational number.
$q: \sqrt{2}$ is an irrational number.
The first statement $p$ is false,as $\sqrt{2}$ cannot be expressed in the form $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$.
The second statement $q$ is true.
Since the connecting word is 'or',the compound statement is true if at least one of the component statements is true. Therefore,the compound statement is true.
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