State whether the "Or" used in the following statement is "exclusive" or "inclusive". Give reasons for your answer.
To apply for a driving licence,you should have a ration card or a passport.

The contrapositive of "If $x$ and $y$ are integers such that $x y$ is odd,then both $x$ and $y$ are odd" is

The following statement $(p \to q) \to [(\sim p \to q) \to q]$ is

Given below are two pairs of statements. Combine these two statements using "if and only if".
$p:$ If the sum of digits of a number is divisible by $3,$ then the number is divisible by $3.$
$q:$ If a number is divisible by $3,$ then the sum of its digits is divisible by $3.$

The expression $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$ is equivalent to

Which of the following is false?