Let $p$ and $q$ be two sub statements of the compound biconditional statement given as $p$⇔$q$.
The negation of this biconditional statement is given as ($p$^~$q$)∨($q$^~$p$)
In the above statement, is the OR(∨) separating the two sub statements in parenthesis exclusive OR or inclusive OR?
Please help. Much thanks in advance 🙂 Regards.
Best Answer
∨ generally means inclusive 'or' (the mathematical 'or'), and this is the case here.
$p \Leftrightarrow q$ means either both $p,q$ are true or both $p,q$ are false; in other words, they always have the same true value. The negation of this is when one is true and the other false, which is precisely what you've written.
That said, it shouldn't really matter because you can't have both $p \wedge\sim q$ and $\sim p \wedge q$, for that would mean you have $p\wedge \sim p$ (and $q\wedge\sim q$) which can never be.