SOLUTION: Set Theory- Cardinal numbers and polls Word Problem A singer-songwriter writes and produces albums for various musicians. Last year I worked on 10 projects. He wrote and produced

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Question 1164082: Set Theory- Cardinal numbers and polls Word Problem
A singer-songwriter writes and produces albums for various musicians. Last year I worked on 10 projects. He wrote and produced 2 projects. Wrote a total of 5 projects. Produced a total of 7 projects. a) How many projects did you write, but did not produce? b) How many projects did you produce, but did not write?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Part of the condition tells about a singer-songwriter,

while another part points to me, using the word "you".

But I am not the above-mentioned singer-songwriter  (and never was).


Can you concentrate all your attention and to write  (re-write)  your post in a  CONSISTENT  manner ?


Please remember that you write to the Math forum,  which requires/assumes  a certain level of accuracy.


===============


Hey, I got your comment with the new version of your problem, which is below 

    A singer-songwriter writes and produces albums for various musicians. Last year, he worked on 10 projects. 
    He wrote and produced 2 projects. He wrote a total of 5 projects. He produced a total of 7 projects. 
    a) How many projects did he write, but did not produce? b) How many projects did he produce, but did not write?


My response : 

There is a universal set of 10 projects.


There is the subset P of 7 projects ("produced").

There is the subset W of 5 projects ("wrote")


Their intersection  (P ∩ W) consists of 2 projects ("wrote and produced").



               Questions :



a)  How many projects did he write, but did not produce? 

        This set is  the difference of subsets  W \ (P ∩ W),  and it consists of 7-2 = 5 projects.    ANSWER



b)  How many projects did he produce, but did not write?

        This set is  the difference of subsets  P \ (P ∩ W),  and it consists of 5-2 = 3 projects.    ANSWER

Solved.