A U (B ∩ C)I

Substitute A={1,3,5,7,9} B={6,7,8,9} C={4,5,6,7}

{1,3,5,7,9} U ({6,7,8,9} ∩ {4,5,6,7})I

Work inside the parentheses first. INTERSECTION or ∩ means to 
use ONLY those elements that are in common to the sets on both 
sides of ∩. Only the 6 and 7 are common to both {6,7,8,9} and {4,5,6,7} 
so we replace the parentheses with just this {6,7}

{1,3,5,7,9} U {6,7}I

Now the I above the {6,7} means to get the complement
set of {6,7} which mean that we are to use all the elements
in the universal set EXCEPT 6 and 7, so they are {1,2,3,4,5,8,9}
So we substitute {1,2,3,4,5,8,9} for {6,7}I

{1,3,5,7,9} U {1,2,3,4,5,8,9}

Now UNION or U means to take all the elements that are on EITHER
side of the U whether it is in common or not.  We just don't
write any element but just one time. So we have the final set:

 {1,2,3,4,5,7,8,9}
  
There are 8 elements.

Answer: 8

Edwin