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

Answer

To solve the problem step by step, we will use the information provided about the number of pupils playing chess and cards, as well as those playing both games.

### Step 1: Define the Sets
Let:
- \( A \) = the set of pupils who play chess
- \( B \) = the set of pupils who play cards

### Step 2: Identify the Given Information
From the problem, we have:
- Total number of pupils = 45
- Number of pupils who play chess, \( N(A) = 21 \)
- Number of pupils who play cards, \( N(B) = 23 \)
- Number of pupils who play both games, \( N(A \cap B) = 5 \)

### Step 3: Find the Number of Pupils Who Play Cards Only
To find the number of pupils who play cards only, we need to subtract the number of pupils who play both games from the total number of pupils who play cards.

The formula to find the number of pupils who play cards only is:
\[ N(B \text{ only}) = N(B) - N(A \cap B) \]

### Step 4: Substitute the Values
Now, we substitute the values we have into the formula:
\[ N(B \text{ only}) = N(B) - N(A \cap B) = 23 - 5 \]

### Step 5: Calculate the Result
Now, we perform the calculation:
\[ N(B \text{ only}) = 23 - 5 = 18 \]

### Final Answer
Thus, the number of pupils who play cards only is **18**.

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