Question 868439


I'm assuming that your initial problem is  *[Tex \Huge \overline{(A \cap B)} \cup \overline{(A \cup B)}]




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 


<font color="red">{2, 3, 4, 5}</font>


which is the final answer.