In a class there are 15 students. 8 of them like playing soccer , 6 of them like swimming , and 2 like both and swimming and playing soccer. how many students do not like either playing soccer or swimming?

There are 3 students who do not like either playing soccer or swimming and it can be determined by using set operation.

Given that,

In a class, there are 15 students. 8 of them like playing soccer, 6 of them like swimming, and 2 like both and swimming and playing soccer.

We have to determine,

How many students do not like either playing soccer or swimming?

According to the question,

Let x be the number of students who do not like either playing soccer or swimming.

Total number of students = n(U) = 15

Number of students who like playing soccer = n(A) = 8

Number of students who like swimming = n(B) = 6

Then,

The number of students like both = 2

Number of students who like swimming = Total number of students who like swimming - number of students like both

Number of students who like swimming  = 6 -2 = 4

And Number of students who like playing soccer = Total number of students who like playing soccer - number of students like both

Number of students who like swimming  = 8 -2 = 6

Therefore,

The total number of students = Number of students who like swimming + Number of students who like swimming + Number of students who do not like either playing soccer or swimming.

Hence, there are 3 students who do not like either playing soccer or swimming.

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