I need some help with this sets question. In a survey in a sampl of students who wrote at least one of the?

subjects P, Q and R yielded the following data. 36 students wrote P, 42 students wrote Q, 38 students wrote R, 9 students wroted both P and R, 8 students wrote P and Q, 12 students wrote Q and R, 26 students wrote Q only and x students wrote all three.


Determine the value of x?


How many students were in the sample?

I need some help with this sets question. In a survey in a sampl of students who wrote at least one of the?
Draw a diagram like this one:





http://i26.tinypic.com/2pt2erm.gif





I've labeled each section with the number of students in that section. For example, 19+x students wrote P only.





We also know that 26 wrote Q only, so from the diagram we have





22 + x = 26


So x = 4





(You should put this value for x into the diagram and confirm that the result agrees with the numbers given in the question.)





I leave the last question to you.