In a class of 45 pupils ,21 play chess , 23 play cards and 5 play both the games . Find
how many play chess play ,

Answer

To solve the problem of how many pupils play chess only, we can follow these steps:

### Step 1: Understand the given information
We have:
- Total pupils = 45
- Pupils who play chess = 21
- Pupils who play cards = 23
- Pupils who play both games = 5

### Step 2: Define the sets
Let:
- Set A = Pupils who play cards
- Set B = Pupils who play chess

From the information given:
- |A| (number of pupils who play cards) = 23
- |B| (number of pupils who play chess) = 21
- |A ∩ B| (number of pupils who play both games) = 5

### Step 3: Use the formula to find pupils who play chess only
To find the number of pupils who play chess only, we can use the formula:
\[ \text{Number of pupils who play chess only} = |B| - |A ∩ B| \]

### Step 4: Substitute the values into the formula
Now, substituting the values we have:
\[ \text{Number of pupils who play chess only} = 21 - 5 \]

### Step 5: Calculate the result
Now, perform the subtraction:
\[ \text{Number of pupils who play chess only} = 16 \]

Thus, the number of pupils who play chess only is **16**.

### Summary of Solution
- Total pupils who play chess only = 16

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