Question

Let A ={1,2).list all the relation on A ​

Answer 1

Answer:

Any relation on A can be written as a set of ordered pairs.  

The only ordered pairs which can possibly be included are  

(a,a), (a,b), (b,a), (b,b).  

If we treat this list of possible ordered pairs as a set, then each relation consists of a subset of them.  

There are 4 ordered pairs in the set, and each subset is a unique combination of them.  

Each unique combination (that is, each relation on A) either includes or excludes each of the ordered pairs (2 choices for each of 4 ordered pairs), so there are  

2^4 = 16 different relations on A.  

Here's the list:  

{ } [the empty set]  

{(a,a)}  

{(a,b)}  

{(a,a), (a,b)}  

{(b,a)}  

{(a,a), (b,a)}  

{(a,b), (b,a)}  

{(a,a), (a,b), (b,a)}  

{(b,b)}  

{(a,a), (b,b)}  

{(a,b), (b,b)}  

{(a,a), (a,b), (b,b)}  

{(b,a), (b,b)}  

{(a,a), (b,a), (b,b)}  

{(a,b), (b,a), (b,b)}  

{(a,a), (a,b), (b,a), (b,b)}  

hope this will help u

Answer 2

Hey buddy I found ur answer in a book.... Happy to help uh