How to negate a bi-conditional statement/exclusive or statement?

lulu

How would you negate "Ann will either take a leave of absence from Technocomp and return in a year or else she will quit her job there".?

Zeke21HeEatin

A := Anne taking leave of absence from Techno and returning in a year
B := Anne quitting her job at Techno

original statement ==> A ------> B

negated ==> A ------> B

which is logically equivalent to
A and B

In other words, it is not the case that Anne will take a leave of absence from Techno and return in a year and it's also not the case that Anne will quit her job at Techno.

Hope that helps

Zeke21HeEatin

In this case it wouldn't really make sense I don't think but to better answer your question I'll attempt to explain it - to negate an exclusive or you're saying that it's not the case that either of those conditions will happen alone. If you watch J.Y.'s truth table video on it it might make more sense but you're basically saying the only two cases that Anne will have after the negation are the case where she neither takes a leave of absence from Techno and returns in a year nor quits her job at Techno (which I diagrammed above). Or the second case, where you're saying that she will do both of those things, i.e., Anne will take a leave absence from Techno and return in a year and she'll also quit her job at Techno. Which is why I'm questioning whether it makes sense to even consider the second case lol. But that's how the logic works out.