Identify the type of Or used in the following statements and cheek whether the statements are true or false:(i) $\sqrt{2}$is a rational number or an irrational number.(ii) To enter into a public library children need an identity card from the school authorities.(iii) A rectangle is a quadrilateral or a 5-sided polygon.

Solution: (i)$\sqrt{2}$is a rational number or an irrational number.
a)$\sqrt{2}$is a rational number.$\to False$
b) $\sqrt{2}$is an irrational number.$\to True$
Out of these two statements, only one statement can be true.
So, type of this statement is $Exclusive$ $OR$.
As, one of the statement is true, so this statement is true.

(ii) To enter into a public library children need an identity card from the school or a letter from school authorities.
a) To enter into a public library children need an identity card from the school.
b) To enter into a public library children need a letter from school authorities.
Both of these satatements can be true.
So, type of this statement is $Inclusive$ $OR$.
Also, both of these statements are false as to enter into a public library children do not need any permission from school.

(iii) A rectangle is a quadrilateral or a 5-sided polygon.
a)A rectangle is a quadrilateral. $\to True$.
b)A rectangle is a 5-sided polygon.$\to False$
Out of these two statements, only one statement can be true.
So, type of this statement is $Exclusive$ $OR$.
As, one of the statement is true, so this statement is true.