A,Band C are three sets.C is a subset of B ;n(AuBuC)=58; n(BuC)=35;n(BnC)=22;?

n(AnC)=10; n(A)=40 and n(B')=23 Draw a venn diagram to represent the information

A,Band C are three sets.C is a subset of B ;n(AuBuC)=58; n(BuC)=35;n(BnC)=22;?
Draw the Venn diagram with 3 circles A , B, and C overlapping.


since C is a subset of B then there are 22 items in C that are also in B (from B and C = 22 ) to place these into your diagram. of these 22 there will be 10 of the items in set A as A intersects C = 10...so place these into set A and set B and set C ==%26gt; this is the intersection of all the sets ! the remaining 12 go into C and B intersection. Since the complement of B is 23 that means that 23 items could be in A (or outside and in the universal set) and not in either C or B (cover up set B and then see where these 23 items will be placed in your drawing,,,not in C as that is all in B remember? so some of these 23 will be in A or some outside all the sets in the universal set...put them in A for now...then we will find out ...Since set A has 40 and B 35 there could be 13 in A and B (we already have 10 there in the intersection of all three sets and 13 in A and B but not C). The last piece is coming now...B union C has 35 so this means that there are 13 in B that are also in A ....and A has 40 (add in the intersection of all three and you will see what is missing ...there are 4 more in A that are not in B or in C) if there is a total of 58 in all then there must be 6 items floating outside of these sets in the universal set (check this from the complement of B)





The diagram should be completed now....when working a Venn Diagram it usually is best to start in the center at the intersection of all sets...then work out with the intersections of the sets 2 at a time and finally each set and then the remaining items that are not in any of the sets but are in the universal set .





This may sound confusing but if you draw the Venn and work it out from the inside and label as you go along..use a pencil as you may erase sometimes... :-) This will work.





Good Luck !