Identify the type of "Or" used in the following statement and check whether the statement is true or false:
"$A$ rectangle is a quadrilateral or a $5$-sided polygon."
"$A$ rectangle is a quadrilateral or a $5$-sided polygon."
(N/A) The statement is composed of two component statements:
$p$: $A$ rectangle is a quadrilateral.
$q$: $A$ rectangle is a $5$-sided polygon.
Here,the "Or" used is exclusive because a rectangle cannot be both a quadrilateral and a $5$-sided polygon simultaneously.
Since $p$ is true and $q$ is false,the disjunction $p \lor q$ is true.
$p$: $A$ rectangle is a quadrilateral.
$q$: $A$ rectangle is a $5$-sided polygon.
Here,the "Or" used is exclusive because a rectangle cannot be both a quadrilateral and a $5$-sided polygon simultaneously.
Since $p$ is true and $q$ is false,the disjunction $p \lor q$ is true.
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Which of the following statement$(s)$ is/are not true?
$I$) If $1$ is not a prime number, then $2$ is not a prime number.
$II$) $e$ is a vowel and $12 \times 3 = 36$.
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$III$) It is not true that $14$ is a composite number and $3$ is an even number.
$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.
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