Not long ago I finished a project for a school assignment. After the assignment was done I left the office of this particular teacher. Just before I wanted to exit through the door I turned around and asked if he preferred the door open or close. The question I asked was "Door open or door closed?". This particular teacher always tries to be funny in a dickish way. He answered "Yes". After some research I found out that apparently the answer yes to an or question is valid, because "or" in a question is like the programmable "or". How would I ask exclusively "or" questions, programmable xor, so to speak.

TLDR: How to ask "Xor" questions in english, A Xor B.

  • 1
    "Shall I leave the door open, or shall I close it?" — What you do then is ask two questions, to which yes or no would be an invalid answer. Outside questions, you can often use either x or y. – Cerberus_Reinstate_Monica Apr 20 '14 at 2:54
  • This question appears to be off-topic because it is about logic, not language. – FumbleFingers Apr 20 '14 at 16:28

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.

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