/sci/ - Science & Math » Thread #12380505

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can /sci/ solve this?

Anonymous Tue 24 Nov 07:27:23 2020 No.12380505 View Reply Original Report

Quoted By: >>12380542 >>12380578

Let M be a set.
This exercise is about binary operations:
M × M M on M.

Let |M| = 2.
How many such binary operations are commutative? Explain it

Anonymous

Anonymous Tue 24 Nov 2020 07:29:30 No.12380508 Report

Quoted By:

correction in line 3:
M × M M on M

Anonymous

Anonymous Tue 24 Nov 2020 07:30:33 No.12380511 Report

Quoted By:

correction

M × M ---> M on M

Anonymous

Anonymous Tue 24 Nov 2020 07:42:29 No.12380542 Report

Quoted By:

>>12380505
any group of size 2 is Abelian

Anonymous

Anonymous Tue 24 Nov 2020 07:57:30 No.12380578 Report

Quoted By:

>>12380505
8

Anonymous

Anonymous Tue 24 Nov 2020 08:03:37 No.12380584 Report

Quoted By: >>12380588

Set M = {a, b}, M x M = {(a,a), (a, b), (b, a), (b, b)}
(a,a) and (b,b) are trivially commutative for any relation. Therefore, we just need to look at in how many ways we can assign (a,b) and (b,a) to same element. That's in two ways. So the total amount is 2*4 = 8 where 4 came from the fact that how we assign (a,a) and (b,b) is irrelevant but needs to be counted. That's 4 ways.

Anonymous

Anonymous Tue 24 Nov 2020 08:04:54 No.12380588 Report

Quoted By:

>>12380584
Actually, does the relation have to be onto? If yes, then 6.

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