I try to divide the problems to sub-problems.

The set S contain four element {0, 1, 2, 3}. n = 4. n = number of element

a,b,(a+b) is in the set.

Why the number of equations in S that have: a+b=b+a is n*(n+1)?

In the set operation 4*5=20.

There are 20 equations that:

0+1=1+0

1+1=1+1

...

I repeat on the question to be clear:

Why the number of exercises (with the + operation) is the number of element of S (n) multiplied by (n+1)?

If You don't understand, explain to me what sentence you don't understand(!!) so I will fix it...