Given the universal set U = {x | xЄ N ^ x ≤ 20} and the sets A, B and C?

where A = {1, 2, 5, 13}, B = {x | x is an odd number}, C = {x | x ≤ 13};





a) draw a venn diagram showing A, B, C and their contents


b) list the contents of : -





1 - C'∩ (B ∪ A)


2 - B ∪ C


3 - A ∩ B ∩ C


4 - C \ B

Given the universal set U = {x | xЄ N ^ x ≤ 20} and the sets A, B and C?
Let's figure out what they are:





A = {1,2,5,13}


B = {1,3,5,7,9,11,13,15,17,19}


C = {1,2,3,4,5,6,7,8,9,10,11,12,13 }





I'm not sure what AB means. I assume that either means the intersection of A and B, written A∩B, or something else.





AB = A∩B = {1,5,13}


AC = A∩C = {1,2,5,13}


BC = B∩C = {1,3,5,7,9,11,13}


ABC = A∩B∩C = {1,5,13}





Notice that A∩C = A. That means A⊂C.


This is the reason that A∩B = A∩B∩C.








Upon completing this question, I think you want the exclusive intersection, meaning AB = {x : x is in A and B, but nothing else}. Here's what that looks like:





A = { }


B = {15,17,19}


C = {4, 6, 8, 10, 12}


AB = A∩B\C = { }


AC = A∩C\B = {2}


BC = B∩C\A = {3,7,9,11}


ABC = A∩B∩C = {1,5,13}





So. Let's draw our diagram:


http://math.colgate.edu/~kellen/interspa...





Then we use our diagram for these questions:





## 1: C'∩ (B ∪ A)





So, we need something NOT in C, but in either A or B.


http://math.colgate.edu/~kellen/interspa...


{15,17,19}





## 2 B∪C





Anything in B or C:


http://math.colgate.edu/~kellen/interspa...





{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 19}





## 3: A ∩ B ∩ C





Things in all three of A, B, C.


http://math.colgate.edu/~kellen/interspa...


We already did this one:





{1, 5, 13}





## 4: C \ B


http://math.colgate.edu/~kellen/interspa...


Stuff in C, but not in B:





{2, 4, 6, 8, 12}
Reply:We can't draw Venn diagrams on here. Just draw three intersecting circles, label them A, B, and C, and write the correct elements in the correct parts of the circles.





C' ∩ (B ∪ A) "not C and (B or A)":


B U A = 1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19


C' ∩ (B ∪ A) = 15, 17, 19





B U C "B or C":


= 1, 3, 5, 7, 9, 11, 13, 15, 17, 19





A ∩ B ∩ C "A and B and C":


= 1, 5, 13





C \ B "C but not B":


= 2, 4, 6, 8, 10, 12