Participation in sports is compulsory in a school and A class has `80` student out of which `60` students play football and `40` subjects play basketball. Find how many students.
`(a) ` play football only,
`(b)` play basketball only,
`(c )` Play both football and basketball.

Answer

To solve the problem, we will use the principle of set theory. We have the following information:

- Total number of students (S) = 80
- Number of students who play football (F) = 60
- Number of students who play basketball (B) = 40

Let \( x \) be the number of students who play both football and basketball.

Using the principle of inclusion-exclusion for sets, we can express the total number of students as:

\[ S = F + B - x \]

Substituting the known values into the equation:

\[ 80 = 60 + 40 - x \]

Now, we can simplify this equation:

\[ 80 = 100 - x \]

Rearranging gives:

\[ x = 100 - 80 = 20 \]

So, the number of students who play both football and basketball is \( x = 20 \).

### (a) Students who play football only:

To find the number of students who play football only, we subtract the number of students who play both sports from the total number of students who play football:

\[ \text{Students who play football only} = F - x = 60 - 20 = 40 \]

### (b) Students who play basketball only:

Similarly, to find the number of students who play basketball only, we subtract the number of students who play both sports from the total number of students who play basketball:

\[ \text{Students who play basketball only} = B - x = 40 - 20 = 20 \]

### (c) Students who play both football and basketball:

As calculated earlier, the number of students who play both football and basketball is:

\[ \text{Students who play both} = x = 20 \]

### Summary of Results:

- (a) Students who play football only: **40**
- (b) Students who play basketball only: **20**
- (c) Students who play both football and basketball: **20**