SOLUTION: If Set A has 9 letters and 3 numbers. Set B has 12 letters and 1 number. 9 letters and 1 number is common to both sets. What is the number of elements in set A or set B?

Draw two overlapping circles, label one A and one B, like this



First look at these words:

Letting L stand for a letter and N stand for a number,
put 9 L's and 1 N in the part in the middle which is 
common to both circles, like this:



Next look at these words:

Set A already has 9 letters and 1 number because they are in the part
that is in common to both circles.  So set A needs 2 more numbers so
it will have 3 numbers.  (It doesn't need any more letters).  So we
put 2 N's in the left part of A, like this:

 

and now set A has 9 letters and 3 numbers.

Next we look at these words:

Set B already has 9 letters and 1 number because they are in the part
that is in common to both circles.  So set B needs 3 more letters so
it will have 12 letters.  (It doesn't need any more numbers).  So we
put 3 L's in the right part of B, like this:



and now set B has 12 letters and 1 number.

Now the question is:

If we count all the L's and N's that are in either one of the
two sets, we see there are 12 L's and 3 N's, so that makes 15
elements.

Answer: 15 elements.

Edwin