Question

In a group of 10 students, 6 study Mathematics, 5 Theology, and 7 French. 3 study Maths and Theology, 2 study Theology and French, and 4 study French and Maths. (A) How many study all three subjects?

A. (A) 1
B. (B) 2
C. (C) 3
D. None of the above

Answer 1

To find the number of students who study all three subjects (M ∩ T ∩ F), we can use the principle of inclusion-exclusion.

Step-by-step explanation:

To determine the number of students who study all three subjects, we need to find the intersection of the sets representing each subject. Let's label the sets as follows:

Mathematics (M) = 6 students

Theology (T) = 5 students

French (F) = 7 students

Maths and Theology (M ∩ T) = 3 students

Theology and French (T ∩ F) = 2 students

French and Maths (F ∩ M) = 4 students

To find the number of students who study all three subjects (M ∩ T ∩ F), we can use the principle of inclusion-exclusion:

M ∩ T ∩ F = |M| + |T| + |F| - |M ∩ T| - |T ∩ F| - |F ∩ M| + |M ∩ T ∩ F|

Substituting the given values:

M ∩ T ∩ F = 6 + 5 + 7 - 3 - 2 - 4 + |M ∩ T ∩ F|

Simplifying the equation:

M ∩ T ∩ F = 9 + |M ∩ T ∩ F|

Therefore, there are 9 students who study all three subjects.