Thread: Puzzle Time:

So here is another nice little puzzle based on set theory, with a perfectly plausable senario.

Ok so the puzzle goes like this, imagine you have an office where everybody drinks coffee,
they all drink coffee everyday, and they get their coffee in exactly one of two ways:

Option A) Either they go and make it themselves, or
Option B) The secretary makes it for them.

Another way to explain this is:

The secretary is only person in the office who makes coffee for those who don't make it
themselves.

The question is: Who makes coffee for the secretary and which option is this?

She makes it herself and I want to say both options, but you say exactly one of two options, so I'd guess option A.

The barber!

The answer depends on whether the "or" between Option A and B is an inclusive or and an exclusive or. In the latter case, the statement of the puzzle is logically inconsistent.

This situation causes a lot of trouble for sets that "are members of themselves." The set of all sets provides built-in logical inconsistencies.

Originally Posted by KALSTER

She makes it herself and I want to say both options, but you say exactly one of two options, so I'd guess option A.

Well that's a really good try Kal, and will be really interesting to see a few answers at this one.

Originally Posted by Dywyddyr

The barber!

You are far to clever for me I'm afraid lol. Well done.

Originally Posted by mvb

The answer depends on whether the "or" between Option A and B is an inclusive or and an exclusive or. In the latter case, the statement of the puzzle is logically inconsistent.

This situation causes a lot of trouble for sets that "are members of themselves." The set of all sets provides built-in logical inconsistencies.

Can you explain the logical inconsistency? If the secretary only makes coffee for those who don't make it themselves, and she definitely drinks coffee, then only she can make it. Since she makes it herself, I'd say that disqualifies her from option B, provided the essence of option B is not necessarily that she makes it, but that the person drinking the coffee didn't.

Originally Posted by KALSTER

Can you explain the logical inconsistency?

She can't make it for herself because it's specified that she only makes coffee for those who DON'T make it for themselves. Ergo, someone else must make it for her. But:
It's also specified that she is the ONLY person to make coffee for those who don't make it for themselves - thus no one else can make it for her.It's insoluble.

Take a look at Russell's Paradox or the simpler (i.e. it's in plain English) Barber Paradox.

It's the inclusive/ exclusive "or" that's thrown you off. Maybe a better way to state it would be:

The secretary is only person in the office who only makes coffee for those who don't make it
themselves.

The question is: Who makes coffee for the secretary and which option is this?

That precludes her from making her own coffee.

Let me repeat the options so that they are in front of us:

Option A) Either they go and make it themselves, or
Option B) The secretary makes it for them.

There are two possible meanings of "or." The inclusive or means that A or B is correct and that both may be correct. The exclusive or means that A or B is correct but not both. The problem is with the second meaning. Since the secretary makes coffee for herself, option B is true. But the other way of looking at is is that she "goes and makes it for" herself , so that option A is also true. But with exclusive or, we said that they weren't both to be true. Hence we have a problem, and something must have been wrong with the initial statement of the problem.

Edit: Darn, beaten to the punch.

Ah, like I said then, it only works with the rationalisation I provided, but not as stated. Thanks.

Since this is a mathematics forum allow me to dull........

Suppose a set , then this set will be well-defined if and only if any object whatever in the universe of objects, real, abstract or relational is definitely in or definitely. NOT in

So the "complement" of is the set of objects that are definitely NOT in - one writes for this set.

By the definition of well-definedness I gave, it cannot possibly be that , so the Russell paradox is avoided BY DEFINITION