Intensional and extensional definition of sets

I am searc开发者_运维百科hing for a extensional definition for the following set:

E := { m | m subset {a,b,c,d} and |m| = 2}

My idea is

E := {{a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,a}, {b,b}, {c,c}, {d,d}}

any ideas?

Most of the time sets are unordered and do not contain duplicate elements. So the answer really depends on how you define sets. If sets cannot contain duplicates, then {a,a} is really {a}, and so |{a,a}| = 1

So my advice to you is look back on the way sets are defined for your particular assignment and whether order and/or duplicates matter for your particular definition. Most of the time they don't but in your case they might.