Given these sets:
A = {1,2,3,4}
B = {3,4,5,6,7}
C = {3,5,7,9}
list the elements of this set:
C⋂(A⋃B)
Spread that out so we can substitute the sets for the letters:
C ⋂ ( A ⋃ B )
{3,5,7,9} ⋂ ( {1,2,3,4} ⋃ {3,4,5,6,7} )
First we work inside the parentheses. ⋃ (union) means to take all the
elements that are in either set, whether they are in common to both
sets or not. So (A⋃B) will contain 1,2,3,4,5,6,and 7. So we write
this next:
{3,5,7,9} ⋂ ( {1,2,3,4,5,6,7} )
Now we don't need the parentheses any more, so we erase them:
{3,5,7,9} ⋂ {1,2,3,4,5,6,7}
Now ⋂ (intersection) is more restrictive than ⋂. It means to take ONLY
the elements that are IN COMMON to both sets and take no other elements.
The only elements that are in both sets now are 3,5, and 7, so the
answer is
{3,5,7}
Edwin