The question asks to find the number of students who read both Mathematics and English, denoted as n(M ∩ E) = x. The image shows calculations related to a set theory problem involving students reading Mathematics and English.

• Total number of students in the class, $n(U) = 40$.
• Number of students who read Mathematics, $n(M) = 30$.
• Number of students who read English, $n(E) = 20$.
• Number of students who read both Mathematics and English, $n(M \cap E) = x$.

Based on the given values, the regions in the Venn diagram should be:

• Students who read only Mathematics: $n(M \text{ only}) = n(M) - n(M \cap E) = 30 - x$.
• Students who read only English: $n(E \text{ only}) = n(E) - n(M \cap E) = 20 - x$. (Note: The $90-x$ in your diagram for "only English" is incorrect; it should be $20-x$ based on $n(E)=20$).
• Students who read both Mathematics and English: $n(M \cap E) = x$.

Assuming all students read at least one subject (i.e., there are no students who read neither), the total number of students $n(U)$ is the sum of the students in each distinct region of the Venn diagram.
The formula you wrote, $n(U) = n(M) + n(M \cap E) + n(E)$, is incorrect because it double counts the intersection and adds it again. The correct approach is to sum the unique parts of the sets:

Alternatively, using the formula for the union of two sets:

Using the union formula:

Now, solve for $x$:

The number of students who read both Mathematics and English is 10.