SOLUTION: 5. If D = {w, h, y} and E = {n, o, t}then answer the following: (a) How many possible one-to-one correspondences are there between sets D and E? (b) How many elements a

We may choose an elements of E to correspond to w in 3 ways.
We may then choose one of the remaining elements of E to correspond to h in 2 ways.
We must then choose the remaining 1 element of E to correspond to y.

So that's 3x2x1 or 6 ways.  They are

{ (w,n), (h,o), (y,t) }
{ (w,n), (h,t), (y,o) }
{ (w,o), (h,n), (y,t) }
{ (w,o), (h,t), (y,n) }
{ (w,t), (h,o), (y,n) }
{ (w,t), (h,n), (y,o) }
 

(b) How many elements are in the Cartesian product D × E? 

We may choose an elements of E to correspond to w in 3 ways.
We may choose an elements of E to correspond to h in 3 ways. 
We may choose an elements of E to correspond to y in 3 ways.

So that's 3x3 or 9 elements.

D x E = 

{ (w,n), (w,o), (w,t), (h,n), (h,o), (h,t), (y,n), (y,o), (y,t) } 

Edwin