This problem is about Venn Diagrams.
Each yellow point represents a family member.
The diagram "TP" represents the two members who would go to all three places. It has nothing to do with the other sets; that's why it is "alone". Now, the set "NC" represents those members who wouldn't go to the family cottage; the set "NB" represents those members who wouldn't go to the beach; and the set "NP" represents those members who wouldn't go to the park.
the construction of the right diagram was made inside out. I began with those who wouldn't go to any place ( nor beach, nor park, and nor family cottage); they are 4. After that, I considered the "intersection between two sets" (they are highlighted with a blue outline). For example, we know that 7 would go to neither a park nor the family cottage, but we have four of them inside the red outline. Then, there should be only 3 members (yellow points) inside the blue outline between NC and NP. After that, I looked for those members in only one set (They are only in one set); for example, we know that 11 would not go to the family cottage; but we have considered 9 of them before (as you can see in the diagram). Then, there should be only two yellow points belonging only to NC.
Finally, the solution to the problem is just to add up the yellow points in the drawing. The total number of family members is 20.
