Is "and" commutative?

I am looking at two answers to the question "write the equation represents the statement 'the quotient of x and y'". This expression can be translated to an algebraic statement as: "x/y".

My question is: can someone argue that since "apples and bananas" is the same as "bananas and apples", "x and y" is the same as "y and x" and "the quotient of x and y" can also be written as "y/x"?

This is a similar discussion to some extent.

"And" is a conjunction and not a mathematical word, per se. Like all word usage, context is everything.

In your particular example, there is an assumption of mathematical principles that are required to understand the statement.

People understand "the quotient of six and two" to follow the formula "the quotient of [numerator divided by] and [denominator]."

So, no, "and" is not definitively commutative nor does "the quotient of x and y" equal both "x/y" and "y/x."

This is an excellent question because we all learn that, using mathematical logic, 'and' is commutative, but you seem to have found an example, -from- math, where it is not.

For the most part yes, 'and' is commutative in natural English, but there are instances where it is not.

If you shoehorn your instances of 'and' into a technical, stipulative definition, like logical 'and', then it is by definition commutative. In your quotient example though, what is going on? There is a natural (as opposed to stipulative) usage of 'and' that is sequential. 'The quotient of x and y' is taken to be a function of the two parameters, x and y, in that order. And order is not commutative. Change the order and you've changed the meaning.

But of course natural language is not bound by math rules and it could do anything it wants as long as people communicate tolerably well with it. There are numerous instances of 'and' where 'x and y' is not the same as 'y and x'. For example the many binomials eg 'bread and butter', 'thick and thin', 'pots and pans'. You just don't use the other direction. "pans and pots" is understood, but you just don't say it that way.

For a more literal example, the label 'lost and found' as the place to retrieve something you have lost is illogical as 'found and lost', or imaginatively, that's quite a different meaning place altogether.

So for the most part, yes, 'and' is commutative. But there are a reasonable number of patterns where it is not.