How many closed binary operations

Log in. Install the app. For a better experience, please enable JavaScript in your browser before proceeding. You are using an out of date browser. It may not display this or other websites correctly. You should upgrade or use an alternative browser. Thread starter wessleym Start date Oct 1, Joined Sep 29, Messages 6. If f can be extended to A in ways, what is A? I'm not even sure I need this question answered so much as I need to understand extensions. But really, you have taught me very much.

It's just some of the language that seems to get me down. Joined Jan 29, Messages 11, Could a nonempty set include [null] and other integers? For some that I couldn't explain can someone explain to me how answers were achieved?. In this context it's obvious what the total number of operations is. Now we consider commutativity. Before going to the specific condition from your problem, consider the question of how many operations in general are commutative.

I assume you've seen the idea of writing down the table for a binary operation. In these terms, a commutative operation gives a table symmetric about the diagonal. So it's value is determined entirely once you've written all the values on and below the diagonal.

Finally, for the number of total operations that have identity, our first guess should be that it's just five times the number of operations with a given identity a la the first question , as we jsut sum over all possible choices of identity. But we need to check that identities are unique, so that we don't double count, I leave that to you. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. The amount of closed binary operations on A under these conditions are what? Ask Question. Asked 7 years, 3 months ago. Active 7 years, 3 months ago. Viewed 1k times. I am mainly in need of help for the bolded answers that I don't know how the book obtained. Jake Jake 13 4 4 bronze badges.

Will find the link.