well, we have 6 elements in A. How many choices are there to map the first element to? After that, how many choices are there to map the second element to...continue this procedure. The product of all the choices is what you seek.

are you aware of what symmetric means?b.) Determine the number of symmetric relations on there are

here is a symmetric mapping. try to untangle it's secrets:

let the elements of A be a,b,c,d,e,f, the mapping defined by:

a --> b

b --> a

c --> d

d --> c

e --> f

f --> e

is symmetric

this is only the identity, right?c.) Determine the number of reflexive relations on there are