In a class of 40 students , each one plays either Tennis or Badminton or both. If 28 plays Tennis and 26 play Badminton ,find
How many play Tennis only:

Answer

To solve the problem, we will use the principle of sets and the information provided in the question.

### Step-by-Step Solution:

1. **Identify the Sets:**
- Let \( T \) be the set of students who play Tennis.
- Let \( B \) be the set of students who play Badminton.

2. **Given Information:**
- Total number of students, \( |T \cup B| = 40 \)
- Number of students who play Tennis, \( |T| = 28 \)
- Number of students who play Badminton, \( |B| = 26 \)

3. **Use the Formula for Union of Two Sets:**
- The formula for the union of two sets is given by:
\[ |T \cup B| = |T| + |B| - |T \cap B| \]
- Here, \( |T \cap B| \) represents the number of students who play both Tennis and Badminton.

4. **Substitute the Known Values:**
- Substitute the values into the formula:
\[ 40 = 28 + 26 - |T \cap B| \]

5. **Simplify the Equation:**
- Combine the numbers on the right side:
\[ 40 = 54 - |T \cap B| \]

6. **Solve for \( |T \cap B| \):**
- Rearranging gives:
\[ |T \cap B| = 54 - 40 \]
- Therefore,
\[ |T \cap B| = 14 \]

7. **Find the Number of Students Who Play Tennis Only:**
- The number of students who play Tennis only is given by:
\[ |T \text{ only}| = |T| - |T \cap B| \]
- Substitute the values:
\[ |T \text{ only}| = 28 - 14 \]
- Thus,
\[ |T \text{ only}| = 14 \]

### Final Answer:
The number of students who play Tennis only is **14**.

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