Question 320024: 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
A ∩ (B U C)
Note: The "U" in between the B and C is not really a U, but suppose to be a symbol like an uppercase U.
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website!
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
A ∩ (B U C)
Substitute the sets for the letters:
A ∩ [ B U C ]
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{1,2,3,4} ∩ [{3,4,5,6,7} U {3,5,7,9}]
We do the part in [ ] first. To take the union of {3,4,5,6,7} and {3,5,7,9}
and make a set with elements that are in one or the other or both. So
we replace the bracketed expression by {3,4,5,6,7,9}
A ∩ [ B U C ]
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{1,2,3,4} ∩ [{3,4,5,6,7} U {3,5,7,9}]
{1,2,3,4} ∩ [ {3,4,5,6,7,9}]
and that is just
{1,2,3,4} ∩ {3,4,5,6,7,9}
To take the intersection we may use ONLY elements which are in common
to both sets. So the final answer is
{3,4}
because 3 and 4 are the only elements in common to both sets.
Edwin
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