Draw a Venn diagram with three circles, J, B, and T. Each section will contain the number of people in only that section (so the number written in the Times circle, but no other circles is the number of people who only read the Times.) This way, all of our numbers should sum to 113, and the numbers in a circle should sum to the total number of readers of that circle's publication.
So write 42 in the center, JBT, since 42 read all three. Now, 56 read the Journal and Business. We've already counted 42 of them in the center circle, so write 56-42=14 in the section in J and B, but not T.
Now, 67 read the Journal and Times. We've already counted 42 of them in the center region, so write 67-42=25 in the section in J and T, but not B.
Now, all of our numbers lie in J, and they sum to 81. 87 read the Journal total, and we've already counted the 81 who read other things. So 87-81=6 people read only the Journal.
Now, 55 read Business and Times. We've already counted the 42 people in the center, so that leaves 55-42=13 people in T and B, but not J.
Adding the numbers in T gives 80 people who read Times plus other papers. 88 people read Times total, so that leaves 88-80=8 people who read only Times.
Repeating for Business gives 74-69=5 people who read just Business, and our Venn diagram is complete.
Now we can read the rest of the answers off our Venn diagram.
How many read Times or Business? Sum the numbers that lie in either Times or Business, and get 107.
How many don't read Journal? Sum the numbers outside the Journal circle and get 26.
~T (intersect) B=people who both don't read Times and do read Business. Adding the sections outside T and inside B gives 19.
J (union) ~B=people who either read Journal or don't read Business (or both). So adding up the numbers inside J, and then adding the remaining numbers that are outside B gives 95.
