Question

Which among the following options represent correct usage of logical connectives in statements $p,q$
$p$ : A physical quantity is scalar or vector
$q$ : A natural number is even or odd.

• A. ($p$) Inclusive OR, ($q$) Exclusive OR
• B. ($p$) Exclusive OR, ($q$) Inclusive OR
• C. ($p$) Inclusive OR , ($q$) Inclusive OR
• D. ($p$) Exclusive OR, ($q$)Exclusive OR

Answer 1

The correct option is D ($p$) Exclusive OR, ($q$)Exclusive OR

$p$: A physical quantity is scalar or vector
Here If a physical quantity is scalar then it excludes the selection of vector i.e.,both sub statements are not true simultaneously. so, it is ''exclusive OR''.

$q$ : A natural number is even or odd.
Here, if a number is even then it excludes the selection of odd, so it is ''exclusive OR''.
$\therefore$($p$) Exclusive OR, ($q$) ExclusiveOR