The entering class in an engineering college has 34% who intend to major in mechanical engineering, 33% who indicate an interest in taking advanced courses in mathematics as part of their major field of study, and 28% who intend to major in electrical engineering, while 23% have other interests. In addition, 59% are known to major in mechanical engineering, or take advanced math, while 51% intend to major in electrical engineering or take advanced math. Assuming that a student can major in only one field, what percent of the class intends to major in mechanical engineering or electrical engineering, but shows no interest in advanced math?

So here's what I've done so far,

let

M=mechanical engineering

A=Advanced Math

E=Electrical Engineering

P(M)=.34

P(A)=.33

P((M u A u E)')=.23 // I'm not sure about this notation.

P(M u A)=.59

P(E u A)=.51

And what i THINK i need to find is.. P((M u E) intersect A'). am i right there?

So I went through and did inclusion-exclusion on a few of them and found that

P(M intersect A) = .08

P(E intersect A) = .11

At this point, I feel like I have no idea where to go, I feel like I need more information to complete this problem.