Question 768220
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Draw two overlapping circles, label one A and one B, like this

{{{drawing(400,280,-10,10,-7,7,

locate(-7,5.5,A), locate(6.5,5.5,B), 
circle(-3,0,6), circle(3,0,6)


  )}}}

First look at these words:
</pre>
9 letters and 1 number is common to both sets.
<pre>
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:

{{{drawing(400,280,-10,10,-7,7,
locate(-2,0,L),locate(-1,0,L),locate(0,0,L),locate(1,0,L),locate(2,0,L),
locate(-7,5.5,A), locate(6.5,5.5,B),
locate(-1.5,1,L),locate(-.5,1,L),locate(.5,1,L),locate(1.5,1,L),locate(0,-1,N), 
circle(-3,0,6), circle(3,0,6)

  )}}}

Next look at these words:
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Set A has 9 letters and 3 numbers.
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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:

 {{{drawing(400,280,-10,10,-7,7,
locate(-2,0,L),locate(-1,0,L),locate(0,0,L),locate(1,0,L),locate(2,0,L),
locate(-7,5.5,A), locate(6.5,5.5,B), locate(-6,0,N), locate(-5,0,N),
locate(-1.5,1,L),locate(-.5,1,L),locate(.5,1,L),locate(1.5,1,L),locate(0,-1,N), 
circle(-3,0,6), circle(3,0,6)

  )}}}

and now set A has 9 letters and 3 numbers.

Next we look at these words:
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Set B has 12 letters and 1 number.
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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:

{{{drawing(400,280,-10,10,-7,7,
locate(-2,0,L),locate(-1,0,L),locate(0,0,L),locate(1,0,L),locate(2,0,L),
locate(-7,5.5,A), locate(6.5,5.5,B), locate(-6,0,N), locate(-5,0,N),
locate(-1.5,1,L),locate(-.5,1,L),locate(.5,1,L),locate(1.5,1,L),locate(0,-1,N), 
circle(-3,0,6), circle(3,0,6),
locate(5,0,L), locate(6,0,L), locate(7,0,L)

  )}}}

and now set B has 12 letters and 1 number.

Now the question is:
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What is the number of elements in set A or set B?
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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</pre>