Intensional and extensional definition of sets

Question

I am searching 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?

Answer 1

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.