Door open or door closed? is not an XOR in the true sense of it as you are only asking for one input (Yes or No) but XOR requires two inputs.
You are asking two questions already, but still only getting a single response. If you simply negate the response and use it as the second input you are still only working with an OR. Yes and No, No and Yes, this doesn't give enough variation to complete the truth table for OR but because the OR outcome of any pair where one complement is true is true, you don't need to complete the true/true=true. This is not the case for XOR
It can be a straight OR question because with a door any amount of openness is open, zero amount of openness is closed. Due to the exclusivity of door openness you can safely ask Door open? meaning do you want the door left open or not, there are only two sensible responses, Yes or No, although Don't care is a possibility (same as Up to you) but that really means you can ignore the result of the question and take no action.
The right way to ask in this case is just to ask
Do you want the door left open?
This doesn't work where there is no exclusivity built into your question, for example Shall I leave the book on the shelf or on the floor? cannot be shortened to Shall I leave the book on the shelf?
So that got me thinking, is it really possible to use XOR in English
Can it really be done as an XOR? ... maybe
This is the XOR truth table (bad format alert), Ix is the inputs, R is the result (binary)
I1=0 I2=0 R=0
I1=1 I2=0 R=1
I1=1 I2=1 R=0
I1=0 I2=1 R=1
Lets define the two inputs as 'Your teachers Reply' and 'the Current state of the door'
Lets define the result as Should you change the state of the door
You ask your teacher Door open or door closed? and he replies with either Yes or No.
Our truth table looks like (worse format alert)
Reply Current State of the Door = Should you change the state of the door
No(0) Closed(0) = No(0) (leave the door closed)
Yes(1) Closed(0) = Yes(1) (open the door)
Yes(1) Open(1) = No(0) (leave the door open)
No(0) Open(1) = Yes(1) (close the door)
While we've managed to somehow squeeze a simple English question into an XOR it's not really a proper case for XOR as we've had to 'invent' one of the inputs and I can't think of any English question or statement that would fall into a proper XOR scenario. The problem is always the two positive inputs that result in a negative.
Another possible XOR method
You ask your teacher Door open or door closed?. Ignoring all replies that include responses other than Yes or No we can make some assumptions.
If the reply is just No, that means Door open? No, Door closed? No
If the reply is Yes and No, that means Door open? Yes, Door closed? No
If the reply is just Yes that means Door open? Yes, Door closed? Yes
If the reply is No and Yes, that means Door open? No, Door closed? Yes
Fitting that into our truth table
Reply to Door open Reply to Door closed Result
No(0) No(0) (0) Close the door
Yes(1) No(0) (1) Open the door
Yes(1) Yes(1) (0) Close the door
No(0) Yes(1) (1)Open the door
Again we've had to make something of an assumption, that when the teacher replies with a single response he means that the single response applies to both questions. So it's not at all cut and dried.
After all that I'm beginning to think that the next time you ask your teacher what state he wants his door left in and he answers in a dickish manner, you should find someone in a position of higher authority and tell them he touched you in an inappropriate manner. (Joking)
This could be my next bounty question - find a question that elicits
two answers and a result that fits in to the XOR truth table.
