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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