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.Com
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)   (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.

--------------------------------------------------------------------------
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}

-------------------------------------------------------

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.

-------------------------------------------------------

(A ∩ B)' ∪ (B ∪ C)'

gets updated to

{2, 3, 4, 5} ∪ { }

and that unions to

{2, 3, 4, 5}

which is the final answer.
RELATED QUESTIONS

Guys please Help me solve these two set equation: 1) Let U= {1, 2, 3 ,4, 5, 6}, A= {1, (answered by ikleyn)
Let the universal set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, and the following... (answered by jim_thompson5910)
Given A = {1, 2, 3, 4, 5} B = {2, 4, 6} C = {1, 3, 5} 1. A ∪ B {1, 3, 5} 2. A... (answered by MathLover1)
Match the following. Given A = {1, 2, 3, 4, 5} B = {2, 4, 6} C = {1, 3, 5} 1. A... (answered by Fombitz)
Perform the operation given that B = {−2, 0, 2, 4, 6}, C = {0, 1, 2, 3, 4, 5, 6}, (answered by richwmiller)
Given that p(A)= 1/4 p(B)= 1/5 p(C)= 1/2 Compute the following 1)... (answered by MathLover1)
Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {2, 4, 6}, B = {1, 2, 5, 8},... (answered by Edwin McCravy)
Given A = {1, 2, 3, 4, 5} B = {2, 4, 6} C = {1, 3, 5} 1. 1. A ∪ B 2. 2. A ∪ (answered by MathLover1)
Hello, Here is my question pertaining to elements in a set: Let U = {1, 2, 3, 4, 5, 6,... (answered by lynnlo)