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.

The image shows a problem involving sets and Venn diagrams. You've correctly identified the given values and started setting up the Venn diagram. Step 1: Identify the given information. • 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 E) = x. Step 2: Correct the regions in the Venn diagram. Based on the given values, the regions in the Venn diagram should be: • Students who read only Mathematics: n(M only) = n(M) - n(M E) = 30 - x. • Students who read only English: n(E only) = n(E) - n(M 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 E) = x. Step 3: Formulate the equation for the total number of students. 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 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: n(U) = (n(M) - n(M E)) + (n(E) - n(M E)) + n(M E) Alternatively, using the formula for the union of two sets: n(U) = n(M E) = n(M) + n(E) - n(M E) Step 4: Substitute values and solve for x. Using the union formula: 40 = 30 + 20 - x 40 = 50 - x Now, solve for x: x = 50 - 40 x = 10 The number of students who read both Mathematics and English is 10. x = 10 What's next?