Here's a discussion that might help:
Boss: EMPLOYEE! Did you complete that very important assignment I told you to do yesterday?
Employee: What? You didn't give me a new assignment yesterday! In fact, you weren't even in town.. you were still on vacation, right?
Boss: Look, either you completed the assigned task or you failed to complete the assigned task. Did you complete it?
Employee: No, there wasn't an.. [interrupted]
Boss: ..[interrupting] NO EXCUSES! If you didn't complete it the assigned task, then you failed to complete the assigned task. We're docking your pay!
Employee: Again, Mx. Boss, there wasn't an assignment! You were on the beach without any mobile communication! Look, here's a memo you sent out a week ago informing us you wouldn't be reachable until today!
Boss: Look, employee.. there's this little thing called the Law of Excluded Middle: something's either true or it's not; there's no alterative. So if you didn't complete the assigned task, then you must've failed to complete the assigned task. There's no possible alternative.
Employee: But that's the point of incomplete logic!: we sometimes have things that aren't true or false. For example, I neither succeeded nor failed to complete the assigned task, because, again – THERE WAS NO ASSIGNED TASK IN THE FIRST PLACE!
Boss: You silly employees and your silly nonsensical excuses! You're lucky you have me. Anyway, I know that I've been hard on you, so I'm giving you a real treasure: the world's only 50-tonne golden statue of the taste of a fresh summer ballad, made entirely of platinum and weighing only 10 pounds!
Boss: Yeah, you should've received. Or maybe it's still unreceived?
Employee: It can't be unreceived.. there's no such thing.. that doesn't even begin to make sense..
Boss: You didn't not receive it? Awesome, then you must've received it! The Law of Excluded Middle wins again! But, yeah, you're going to need to pay gift taxes on it, just so ya know.
Later that day:
Boss: Everyone, big news! I proved that 1 is bigger than 2!
Employee: Are you sure that you're okay?
Boss: Yes, yes, I'm great! Better than ever! See, we merely define X, which is a number that's greater than itself plus 2, and.. [interrupted]
Employee: [interrupting] Yeah, I think I see where you're going with this. And that'd be great and everything, except there's no number that's greater than itself plus 2, so that doesn't work.
Boss: So you're saying that X + 1 isn't greater than X + 2?
Employee: No, it's not not greater. But that's moot as there's no such X in the first place.
Boss: If you agree that X + 1 isn't not greater than X + 2, then you agree that X + 1 is greater than X + 2. Then we subtract X from both sides, proving that 1 is greater than 2! Yay for the Law of Excluded Middle!