Practical Problems on Union and Intersection of Two Sets

$E,I,R,O$ denote respectively the sets of all equilateral, isosceles, right angled and obtuse angled triangles in a plane, then which of the following is not true.

In a class of $50$ students, $10$ did not opt for math, $15$ did not opt for science and $2$ did not opt for either. How many students of the class opted for both math and science.

In a school there are $20$ teachers who teach Mathematics or Physics. Of these, $12$ teach Mathematics and $4$ teach both Physics and Mathematics. How many teachers teach Physics?

In a survey of $425$ students in a school, it was found that $115$ drink apple juice, $160$ drink orange juice and $80$ drink both apple as well as orange juice. How many drink neither apple juice nor orange juice?

If $A, B, C$ are three sets and $U$ is the universal set such that $n\left(U\right)=700,n\left(A\right)=200, n\left(B\right)=300$ and $n(A\cap B)=100$. Find $n\left(A^{\text{'}}\cap B^{\text{'}}\right)$.