Question 475209: Let U = {4, 5, 6, 7, 8, 9, 10}, A = {4, 5, 6, 7}, B = {4, 5, 8, 9}, and C = {6, 8, 10}. List all the members of each of the sets. (Enter solutions from smallest to largest. If there are any unused answer boxes, enter NONE in the last boxes.)
(a) A ∪ (B ∩ C)
{ , , , , }
(b) A ∪ (B ∩ C)
{ , , , , }
Can I get a tutor to show the right way to count these? Thank you very much for all of the help!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! A U B = set of the combination of sets A and B
A ∩ B = set of common elements between sets A and B
a)
Since B = {4, 5, 8, 9}, and C = {6, 8, 10}
This means that
B ∩ C = {8}
because 8 is the only thing sets B and C have in common
So
A U (B ∩ C)
becomes
A U {8}
which tells us to simply add the element 8 to set A to get the final answer of
{4, 5, 6, 7, 8}
So A U (B ∩ C) = {4, 5, 6, 7, 8}
For more help with set union and intersection, see this solver.
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