SOLUTION: Let U = {1, 2, 3, 4, 5}, A = {1, 5}, B = {1, 2, 3, 4} and C = {2, 5}. Determine _____ ____ (A∩B)∪(B∪C)

Algebra ->  Conjunction -> SOLUTION: Let U = {1, 2, 3, 4, 5}, A = {1, 5}, B = {1, 2, 3, 4} and C = {2, 5}. Determine _____ ____ (A∩B)∪(B∪C)      Log On


   

Question 868439: Let U = {1, 2, 3, 4, 5}, A = {1, 5}, B = {1, 2, 3, 4} and C = {2, 5}. Determine
_____ ____
(A∩B)∪(B∪C)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

I'm assuming that your initial problem is



I'm going to change the notation to (A ∩ B)' ∪ (B ∪ C)' so I can type it out easier.

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A = {1,5}
B = {1,2,3,4}
The only element that is in BOTH set A and set B is the number 1.

So A ∩ B = {1}

Now find the complement of set A ∩ B. That's basically the set of everything in set U...BUT...we toss out everything we find in set A ∩ B

So we start with U = {1, 2, 3, 4, 5} and delete the element "1" to get (A ∩ B)' = {2, 3, 4, 5}

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B = {1, 2, 3, 4}
C = {2, 5}
Union sets B and C together to get {1, 2, 3, 4, 2, 5} ---> toss out duplicates ---> {1, 2, 3, 4, 5}

Now find the complement of set A ∪ B. That's basically the set of everything in set U...BUT...we toss out everything we find in set A ∪ B

So we start with U = {1, 2, 3, 4, 5} and delete the elements: 1,2,3,4,5 to get (A ∪ B)' = { }

So we're left with the empty set because we tossed out everything in U.

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(A ∩ B)' ∪ (B ∪ C)'

gets updated to

{2, 3, 4, 5} ∪ { }

and that unions to

{2, 3, 4, 5}

which is the final answer.