In a class, 18 students took Physics, 23 students took Chemistry and 24 students took Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics and Mathematics. If 6 students offered all the three subjects, find:
(ii) How many took Maths but not Chemistry.

Answer

To solve the problem of how many students took Mathematics but not Chemistry, we can follow these steps:

### Step 1: Identify the given information
- Number of students who took Physics (P) = 18
- Number of students who took Chemistry (C) = 23
- Number of students who took Mathematics (M) = 24
- Number of students who took both Chemistry and Mathematics (C ∩ M) = 13
- Number of students who took both Physics and Chemistry (P ∩ C) = 12
- Number of students who took both Physics and Mathematics (P ∩ M) = 11
- Number of students who took all three subjects (P ∩ C ∩ M) = 6

### Step 2: Use the formula for students who took Mathematics but not Chemistry
To find the number of students who took Mathematics but not Chemistry, we can use the formula:

\[ \text{Students who took Mathematics but not Chemistry} = \text{Total Mathematics students} - \text{Students who took both Mathematics and Chemistry} \]

### Step 3: Substitute the values into the formula
From the given information:
- Total Mathematics students = 24
- Students who took both Mathematics and Chemistry = 13

Now, substitute these values into the formula:

\[ \text{Students who took Mathematics but not Chemistry} = 24 - 13 \]

### Step 4: Calculate the result
Now, perform the subtraction:

\[ 24 - 13 = 11 \]

### Conclusion
Thus, the number of students who took Mathematics but not Chemistry is **11**.

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