14 notebooks of a class were corrected with ink pen while 22 notebooks were corrected with colour pencil. If 4 notebooks were corrected with both, what is the strength of class?

Options

A. (a) 30
B. (b) 32
C. (c) 28
D. (d) 25

Explanation

To find the strength of the class based on the given information about the notebooks corrected with ink pen and color pencil, we can use the principle of inclusion-exclusion. Here’s how to solve the problem step by step:

### Step 1: Identify the given data
- Notebooks corrected with ink pen (A) = 14
- Notebooks corrected with color pencil (B) = 22
- Notebooks corrected with both ink pen and color pencil (A ∩ B) = 4

### Step 2: Apply the principle of inclusion-exclusion
The total number of notebooks corrected can be calculated using the formula:
\[ \text{Total} = (A + B) - (A \cap B) \]
This formula accounts for the overlap (notebooks corrected with both) by subtracting it once.

### Step 3: Substitute the values into the formula
Now, substitute the values we have:
\[ \text{Total} = (14 + 22) - 4 \]

### Step 4: Perform the calculations
First, add the number of notebooks corrected with ink pen and color pencil:
\[ 14 + 22 = 36 \]
Now, subtract the notebooks corrected with both:
\[ 36 - 4 = 32 \]

### Step 5: Conclusion
Thus, the strength of the class is 32.

### Final Answer:
The strength of the class is **32**.

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